Download unit 9 answer packet

8.3 Trigonometric Ratios
sine, cosine,
tangent io| - c*T1 - ro A
. ^ opposite
side
'^
SmA==
hypotenuse
COSA_
a_
c-
=
'oçroj
b
c-
adjacent side
hypotenuse
q.
opposite side
_
-b
tanA-
adjacent side
Y
3
4
Z
_t_
f
tanY: +
sinX-
If sin A sin45o
5
l,6
then tan A
-- +
sin 30o :
LL
tanMcosN-
_t
IL
5
/3
(r' = st+ x'
-
36 - zl+\z
ll=x2
171
tan 45"
-
tan 60o
-
=x
5in
lp f$^'l
28 =
¿utk¡0")As
sL= #
Å
X = tL(ces tr¡
/(t
X--l(,P2
T6
x-
X-
7.51
l. zt
t^(=T
E
x-
72_.31
o
cosx =T
?l
sin-l
- 'ï1"{ån "oí' ' '!{''!:
Sin X -- -t
2l
X=s¡rí'(+)
The grade of the road is 7Yo. What angle does the road make with
the horizonÍ,al?
-7
tj^^X -- f.ô
tol'(ft)
f, = \.oo
f, =
loo
A rhombus has diagonals that arc 4 meters and 10 meters long.
Find the measures of the angles of the rhombus.
,l
tztvry?l
v
V
LI
=
-
-t r s\
G8. Lo"
Z- (tr
tl =
tZ
zo)
l3G.¿1 "
= 43. G"
'fi
CoS
Lo5
=
2-
IL
lL (cos 6r)
zLl(cos
=Av
-- *
cs)
=
\
z4
(ø" es)
lÇ.to
=!z
7=
J!x
Xl0. tq
2 = 21,36
24
?,
X:
l1.LlE
K-y
31'2:6
-- K
- lb'to
24
CosS
=X
5=-Ez1
þ'- za(a"ss)
F - SLl.Zt
Assignment: p 510 #1 l, 13, 15, 16, 18, 20,21,,23,24, 26,27,29,
29,34,36,38, 48, 53,54
Problems Using Angles of Elevation and Depression
The angle of elevation from a sailboat to the top of
sailboat from the shore?
lighthouse on the shore is 16". How far is the
a
ún
tb
crl?l
-H
t4,¡-lb
'N=
A sonar operator on a cruiser detects
a submarine at a distance
How deep is the sub?
5öÐ
--Ët
¿tLl
.19 +t
of 50O meters and an angle of depression of 37"
x
trrr S7 = .;6
x = (û"
nYÍu)
The grade of the road is SVo. What angle does the road make with the horizontal?
too
Galileo used the "Leaning Tower of Pisa" to conduct his experiments on the laws of gravity. When he dropped
objects from the top of the 55-meter tower, they landed 4.8 meters from the base of the tower, How many
degrees does the tower lean off vertical?
5f-
&^'¡ e -é
{.8
ê=
square based pyramid was uncovered in Egypt.The base is intactand measures 120 meters on a side. The
top portion has eroded away, but what remains of each face of the pyramid forms an angle of 65" with the
ground. V/hat was the original height of the pyramid?
A
þ^^
(t'f
x
'- bo
¡d.il
lY= tz
l---..--
g looks
ngle of
part. A pers
Two buildings are 100 feet apa
building. lf th e angle of elevat
'ation to the
reight of the
the building is 30', find the hei
eet at the other
the bottom
x
åqn
z5=tæ
l. = 4b.
*¡^
3e -- T
IQ
7l
V=
I lo'f
I
.
U3
of
Law of Sines
b
a
sin A
X:
sin
B
sin C
G6.a1
2s
sin
(nnn) = 2o (stnx)
zs (sin *) = gi Ì4 X
z-s
srlt
x:
x
(tt ßnv) \
\Ã-/
=X
l.4.13
t0
5ìn'|L
^.
K
St,n 1
1t
I
ro-þ,vrr) = X
to (stnt)
3M 'lz
-_
(srrt W)
X
o
42;
tul
f,;
l{
7L
= l,^ro
(3M
æ) = 2z'(stnx)
l&l (Srvr fo)
x-
4-
36.81
2L
=
s
jr1 K
lo ut' (* L::'') = x
A surveyor has the job of determining the distance across the Rio
Grande Gorge in northern New Mexico. Standing at one side of
the ridge, she measures the angle formed by the edge of the ridge
and the line of sight to a tree on the other side of the ridge. She
then walks along the ridge 3 15 north and measures the angle
formed by the edge of the ridge and the new line of sight to the
same tree. If the first angle is 80o, and the second angle is 85o,
find the distance across the gorge.
(
V
850
I
É-[
315
--
80"-
J
Sin
3tç
s¡a
Í5 = tllt-,s7
lS
ar (srnæ) = x
Sts ("tnrc)
(rt ø)
("in ts)
à-- (s;nwXn1rs7)
1t14.Ôl
=X
lllÍ.f7
--x
Law of Cosines Notes Filled In.pdf - Page
þ.e law oF
cB:
1
cosINE$
q'[03
'q h= q.ri
fvt
\.Jt
54Iq: I
t¡1
= b-s
LD3ü4 =
F1
n4a{
=t lr
i
= (t/ @S 44
t
cß: {
C-B'
cb
nL + 8,bvL
Law of Cosines Notes Filled ln.pdf - Page 2
\i
iì
Bi
----{ C.-Find the value of
--------ô
a.
L.
I
a- = (c-*f+ht
LC-)LJ T- n
/
/
/
i
t
K= b,l'r,¡ {
I
LL
a- = (,--
&
=ú
\-,
n
tL
LcK+x'+h-
Lctô'sa) *L7-
I
LL
t +L -
1Á.@A
Law of Cosines Notes Filled ln.pdf - Page 3
[,aw of Cosines
MN: La\ Jll
É=
¡nL
-t-4L
.!t -- (zr)t *
fr)t- L(Lilffi)cos(o+)
.f1e551
4' =- 3S\8 -11
A --
[,01,
Law of Cosines Notes Filled ln.pdf - Page 4
-rL
L-
K=V ++. - LY? cos Å
L- [r t)t+ (r, Ðt- LFtXt¿) cpS{
(q
.L
¿)
q5
..L
ù' - (l L)' æ (ro- ¿\L = l LO-l)(a'¿) c.,âsf
t
L.l ¿)L - (-1)t - Lr,-r)
=- acsx
- L(r t)(o'¿)
Law of Cosines Notes Filled ln.pdf - Page 5
*\
P
<.ifl
_r.
t
û'C
rf srn 3L
\.L
t3.w
Ì
.33
Law of Cosines Notes Filled ln.pdf - Page 6
An air fraffic controller is tracking a plane 2.1 kilometers due south
of the radar tower. A second plane is located 3.5 kilometers form
the tower at a heading of N 75'E (75'east of north). Tc the
nearest tenth of a kilometer, how far apart are the two planes?
Plane
D
B
Tow er
b
t
2.1 km
= f+
**
L',bcos D
Plane A
- L(3+lX.^lÓs)
Å1 =
M,4trqN'"
LAW OF'SINES
v:
x
lÔ. ,lL
fv\=¡[.?{ y
æ-
97=
Sin
r1
1
')( r
-- n/t+P
=
ll- 14 +
1'tl
YÉ
tqn 47 =
1'bz -- l0,t1z [ = ll
5,rn t|l
1'?2
f' = ânqz
ry_
sin ^/-A
sin ^/B
-
órn 33 =
x
r
=
?=1.,1
h
(ssn
zs) = J. 6L
(os33=fr
'
?.fl
t^-- tl
(cos
P) = ll.1f
C
h
h- b'slnA
b
h- a-'sin B
I,
4_
-bsinA
sin
A
sin B
Name: Út"
Geometry: Angles of Elevation and Depression
Solve each problem using trigonometric ratios. Show all work.
I
,
A twenty-foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the
building. What angle does the ladder make with the ground?
A
with a cable secured at the top of the tower and tied 30 meters from
the base, V/hat angle does the cable from with the vertical tower?
SO-meter vertical tower is braced
-
\
Ito.rn
x
-
lD
to^-'
5ù
H,
/ /.\,J,
i
,l/,
I ,.;
j
3o
A water slide is 25 meters long and stafts at the top of a tower that is 2l
elevation between the slide and the
ground.
S,,
meters
n'/"|
i
r'
high. Find the angle of
.z-
5l"t'10
)
.)
riangle.
pc"i0O!
7
[;
sì
UJI)r\¿"
vo ,
ì A,^^ot D4
!r]-.,ry
^'
- =tV'.('J),t2'.)
g- = [os
r-J ':-..--,
c'ru
"P'1Ù"
Findtheareaof aparallelogramif onesideis l0cm.,anothersideisScm,andtheanglebetweenthrose
twosidesis{7"' ,-J8-- ,--,
lÙ
i,ud
tn.y',Afl*
¡0.¡:ffrc^
x ll ll-l ¡
à
lr\o5"85
lÙ'5,85 r{-'þ6,Í^2
x=5'65'h*J*
For the right triangle at right, find the following values:
a) sinA= 3
d)sinB= \
b) cosA=
e)
cosB=
Ð
(si
cc
c)
(sin
Þ
A)2
(o.)'
Find the
me
+'
i
B), =
(?Y
in right triangle
ABC
8(6, -
-fnn^A'å ù-qjÐ
8. If the diagonals of a rhombus have lengths of 12 meters and 8 meters,find the measures of the angles of
the
rhombus.
Äþ,
,fttr <{ \
V
\ =9i '2
*o^)'9u "L=
^o
= I l' ' Ue 'Òbfua'îû¿
-ta^
I.rl,3E'crr,rl\(t'¡n(rc
To be used safely a ladder should make an angle of about 75' with the ground.
a)
b)
How far should the foot of a 20-foot ladde
v
How long should a ladder be in order to reach a window that is 36 feet above the ground?
1.
Jb(K
$lrya5
, fu
10.
From the top of a 575-foot high bluff, a rescue scout looks down upon a hot-air balloon accident. The
angle of depression is 7o. How f is the accident from the rescue team at the foot of the bluff?
'ua11
a
I u 1,:'j
o
I
(,
_
.')
1. A road climbs at a 8o angle. What is the grade of the road?
lcr,u-
i
-E' !
tü\)
2
12,
(Give an exact answer) If tan A
(/\a
-I
, then sin
ìr\
s,fã
A = ¿.î"
?¡n,-Þ.^'
"()5'Tn
v-x
\F
, ,r ,'r
\/
;
')
--
\/
"/
.-6r
{-:
13.
A raked
stage is a stage that is slanted toward the audience, like a ramp. In general , a raked stage that
slants much more than 5o is too steep for the actors to move around on easily. Suppose a theater company
builds a raked stage on a stage that is 29 fee¡ deep. If the raked stage is supported at the back by a post
that is 4 feet long and perpendicular to it, at what angle does the stage slant? Is the stage acceptable?
Si^' ï,
14.
4' :l I'
A jet takes off at a 30' angle. The jet's air speed is 200 feet per second.
a.
After l0 seconds what horiz
/.,r \13
?,05Q* .
co__Úo'
I
__Ð_)
X
b.
After 10 seconds what is the jet's altitude?--1)
(+
lfro
J=
vlL'(
-1.
r)ll )t)
;'n'jt)
-----ì
.
)'.i.\
¡) i)
15.
At a point on the ground 50 feet from the foot of
a tree, the angle
Find the height of the tree.
of elevation to the top of the tree is 53".
..-""':-1' '/,
ô.
.íi'
I C)tl-)L'¡'t
ì)
-r
t,J'
ill
(.
r
'j\)
t6.
\
i^
-l
i n
r'
laì, , )'-t-\'t
--'
From the top of a lighthouse 210 feet high, ,nr
of a boat is 27o . Find the distance from
the boat to the foot of the lighthouse if the lighthouse was built at sea level.
@n*trrr,--ù,
0nr
x
17. Richard is flying a kite. The kite string makes an angle of 57o with the ground. If Richard is standing 100
feet from the point on the ground directly below the kite , find the length of the kite string.
/,
.tL,7t
I
(
oi ..'-i
i
i -. ---.f-,1
'f.
I $ ),bl0.r')
ìú\)
ç.lr
18, Anairplanerisesvertically- l000feetoverahorizontal distanceof I mile.-Whatistheangleof
of the äirplane's
path?
=Gr$Qt
r
t¿i!}
¿;f;\)
lfiÐ (.
--/
elevation
( lb ,- t;)'
| ''
)
5l6D (r
19,
The steepest raílway in the world is the Katoomba Scenic Railway in the Blue Mountains of New South
Wales, Australia. A single passenger car is pulled by two steel cables up the length of the railway. The
gradient (or grade) of the railway is l22Vo. What angle does the Katoomba Scenic Railway make with the
horizontal?
-t
-tatt
\?,
',
/,
(.
t/ )
W
/N
\
ì,) \
'
'r ¡\), t, r )" )'
¡¡l.tt
t
Nrme:
'Geometry: Law of Sinos
Krr/
Show all work.
1
.
If mZT =
45o
,
mZE =
63o ,
x
and RE
:22,
then RT
: ?7 "7L
27-
gnllf
5þ'A b3 =
N
2,
=
If RT =3.2,m1T:52o,m.Æ,:'l0o,thenRE
stf' 5z
XÈ
lf mZT
= 2 . Cg
.
3.2
sIYì ?t
_ð_
3.
(sn æ). zz
stn ¿r5
S. 7
10
(s;n sz)
3í"
S¡^'7Ô
= 62o,mZE:26o, and ET =2,6,then RE =
2.0
8 7?- =
2.30
À_
slvt uL
Y!=
If mlR: 7lo;ET = 7 ,4, and mZT
:
mZE: (n8'-
ER:
Å
rh t{l
5.13
RT= 7.26
4lo,
!=
ú
= sin
-71
_-y-bT
sJh
7'1 (svtt\
er^
f=
1-'l
"l
s,X 7l
If mZR = 25o, mZE: 52o, RE = 15.6
mlT: lO3'
ET= G.77
F(T: 17 , GZ
_y
cn6
ts.b
5'h lô3
x-{=
t5. C (s'a zs)
x
5l\\52
The longest side of a triangle is 34 feet. The measures of t\a'o angles of the hiangle are 40o and 65o
Find the lenglh of the other two sides.
g1
_L{o
5M
=
"U
,oS
)/\
C
'
lìYlÛ,l
X* BI(s"Ò=
lof
-
sln
(s¡ qo)
Y-- 31Slrr lof
GRAM is a parallelogram.
MG:
32
ll. 37
Gó
MR= ?-Sl
X
G
Y
tño= 7^u = ¿ t
f,= 6(s¡ntt)
stvtzz = ll '32
v
liY1 3 z
Vince is planning a triangular garden. He wants to put a fence around it. The length of one side of the
garden is 30 feet. If the angles at each end of this side a¡e 44o and 58", find the length of the fence
needed to enclose the garden.
5inq4
? --
3o + z6.ot +
zt.3t
l:
3o
ínÍ)
si¡ 1t
= zl-gl
Two ranger stations 5 miles apart Spot a forest fire, Station A determines that the angle formed by the
line of sight to the fire and the line connecting the two stations is 37o, Station B determines that the
angle formed by tl¡e líne of sight ûo the fire and the line connecting the two stations is 52o, How far is
each station from the fire?
Jn3z1 = '--I
slrt
áh ql
K
sin
3.11
Y=
r,.s,!4 SMcl
3.01
52
I
0.
An isosceles lriangle has
a base
of 22 centimeters and a vertex angle of 36o. Find the perimeter of the
triangle.
xzz
5tn1l
lL
N = Zz (strt zz)
5M 3t
1L
?L
?=
I
l,
lly\ 3U
z(ss.æ) +
- Sf. 6O
:
zz '-l?3-Zou,
Scientists are facking polar bears that have been fitted with radio collars. The scientists have two
stations that are 9 km apart along a straight road, At Station l, the sígnal from one of the collars comes
from a direction of 49o from the road. At Station 2,thesignal from the same collar comes from a
direction 65o from the road. How far is the polar bear from station
2?
starion
I
Polr
f,=
1(srrnrt)
Sin
12.
bcar
Qb
A plume of smoke is spotted from two different frre towers that are 5 mi apart, From Tower A, the
angle between the smoke plume and Tower B is 80o, From Tower B, the angle between the smoke
plume and Tower A is 70o. rühich tower is closer to the smoke plume? How far ís the smoke from the
tower?
Towø
,
þ-
srV
--
SiYl
tÞ
ì
J
sM-to = são
a-
A
þ
-f (s'u Ð
5r'z\
3Ò
Smokc
E0
1tr
1. rto
I
13.
The maximum height that a basketball reaches after being shot is given by the formula
H:
, where
V represents the initial velocity, x represents the degree measure of the angle
which the path of the basketball makes with the ground, and g represents the acceleration due to gravity,
which is 32 feet per second t , Find the maximum height reached by a free-throw if it is shot with an
initial velocity of 25 feet per second at an angle of 650.
H
Fl
14.
(s¡n cç)'
z ( sz #/sù
= (zç l")"
_^
Dee and Bill are standing 100 feet apart and in a straight line with the W\MV television tower, The
angle of elevation from Bíll to the tower is 30o and the angle of elevation from Dee is 20o, Find the
height of the television tower,
Dcc
100
fcct
Bill
Sin L0
x--
l1c.7G {+
11c.lc
++
Name:
Geometry: Law of Sines
V.-"'t
T-
TheLAW OF SINES is o powerful trlongle îool which is used To f lnd missing ¡ldcs or ongles of
ANY triongle. By motching up ongles with their opporltc rldes, the equotion is:
abc
Exomolc: Find the rrissing side x:
sinl9' _ sin40"
L6x
326 _.643
16x
.326x = 10,288
x=3[.56cm
Flnd the tnlssfng sldc
x ln eoch tnlongle:
x ,{o
20
9n
Sh
X (rtacr) = lo (tu, tt)
f, = tlo (su a)
'zç = ìíñtt
_;þ
X
(crn zr
K
,-
) =
Öe
5(^ bZ
zc (stnso)
Zt' (snæ)
<rVì ¿1
).
z
Lll.OS
Xzf
S,h
(s,rael)
73
t'rr
83
-
X
a= zr(snß)
sln
Find thø
t1-tz
lb
sùr
l\
Y-V=
=
\=
J
J-L
srn
11
l{O
X (stn zr) =
t.f")
g^l
loo
úta zl
=
Gy:!.
sln
zl
lll.37
À
a 5l4lo
tu Gn 1o)
x-- |-
t*
31, 11
tôo
(srn no)
Th¿ LAW OF SINES con olso bc us¿d to flnd mlsslng onglcs.
Exonplc: Find th¿ missing
sinxo _ sin75o
36
sin ¡'
36
x:
ongle
c
50
.966
50
50(sinx') =34.776
sinxo
=.69532
v - (!,o
A
(from trig toble)
Flnd thc nlsslng onglc
x
ln coch frfongle:
7'.,
¿11
uo
âin
sln x
+
sin
1o (sM os )
u4 (sn x)
¡
,5,V
5'l .lo "
ît
X -- sin
lzl , e
SrVr
X
--
X
sin
-t ( loç .(si" st)
\ 8s-
l5ó
sîn Z8
¡zr
(stn¿s)
\
lsô /
3t
_þ
--=
51rl x
5;^
lzf
---l
10)
Find the oreo
3l
af(snx) = lol(iust.
s,hX= þ5 (6lY1z't)
Llo (st" æ)
sl'n X è
.E
tÔt
G3
oÍ circleC.
î'çL
Tt
=A
þtu)' = A
ItrsE, to = A
(-ù
GEOMETRY
Review for Test on Trigonometry
Show all work,
t2
B
t2l. sinA= J7
2,
g
cosQ=
t
x
ranR- 7f
tz
tanC=
zL7
t7
35
3, If sinx= I,then cosx=
tanx=
88
sÉ-.
31
-Is1
st+ nL = EZ
x
O"= (tol-25
,-''- 3l
ø.=
fs1
Solve for each variable,
cosst =
\=
#
þMst= *
tS(c"s st)
x= úÌr5/
-f^
x
4, x =
\Z.fuØ
x
= c,rlB
2+
þn =#
¿t,
X = z1 (t^n zc)
15
rectangle
6. x= G+1'1
G'+"
x= \\it
-LZl
X
Sìn
cþs
sìn
loI
y
3l= TtL
=
tz(cos
zs)
fl.t.ES
Î.rs
ú,Yr
g. * =
9^ b5=þ*
f,=
11. x =
ZO'l\
12. ABCD is a rhombus
18
lr,.,,a Q"
nZABC =78
AC= LL,bb
BD =
Cos
?\,q$
13.
*= ?.tO
y=
\\. 2Ø
=*$ +
]-:
j,?l
g
I
âwr.=l tt **o-- '
t4
AB =
x
\2,45
X
sm tlo
10. \b.q tt
=
¿l -
I(>LSv-.,8o"
9r^6t
)L
(x
sq:t
t!
14,
The equal sides of an isosceles triangle are 16 inches. If each base angle is 32 degrees, find
the length of the altitude.
Y
tb
15. A tree casts a 4O-foot shadow at a time when the measure of the angle of elevation of the
!r'nt4Ro,
x
16,
j¡a-r\
X'
tlo
gL1'qzç
vel of ths surrouncling land, a file is sighted at
From a lookout towet 800
How
far is the fire from a point directly underneath
angle
of
of
10
degrees.
an
depression
the tower and on the same level as the surrounding ground?
\oo
17
,
At a point on the ground 80 feet from tl¡e base of a building, the measure of the angle of
elevation to the top of the building is 5l degrees. Find the height of the building,
tu
19. A rhombus
has a
l2 cm side and a76 degree angle, Find the lcrrgths ol
Srnt'"=#
,Þñ
v-- t.b1
eo53fr.-+
\ çÕ
t-
q.,qb
l1 tr
20.
A road climbs at a 5o angle. What is the grade of the road?
Y
B-'lQ{$^.":nù \L--"- --=*-J
--
lsò
I
ì
21. You are flying a kite and have let out 80 meters of string. The kite's angle of elevation
with the ground is 4O degrees. If the string is stretched straight, how high is the kite above
the ground?
Sr". Hb=
l-
bt,4 Z$+
rÒ
I
rx
22. Use what you know about a 30-60-90
triangle to find the exact value for tan 30o.
.-E
¡1^ão'
\3
23.
A helicopter is hovering over a landing pad 100 meters from you are standing. The
helicopter'sangleofelevationwithth_¡:grou¡disl2degrees, Whatisthealtitudeofthe
helicopter?
A.
S,rn r2"
1
=.
toÒ
An airplane climbs at an angle of 18 degrees with the ground, Find the ground distance the
plane travels as it moves 2500 meters through the air.
r
<oS 18 =.7sø
25. You are driving toward a mountain. At a rest stop you use a clinometer (a pocket device
that can rneasure the angle of elevation) to measure the angle of inclination from your eye
to the top of the mountain. The angle measures 11 .5o. You then drive toward the mountain
on level ground for 5 miles, You stop and measure the angle of inclination to 27 .5". Find
the height of the mountain,
lt,
/
slrl zt.s = *,,
26. Giventhe following triangle. Explain wny I
e-ao
=
tiÏB
*{.TEST QUESTI ON'll.,|.
*
st',r l'+ =
I
3in g= þ
l^
= sufi' b
Ja
= sdn8'<
T-rans;'þr- ?r'7.rlY
2t. o=
süitffi p'fl
.zB
to,
ñ
s1
= Sòn 6î.oa'
=
mZA =
10.51
t7' 3
sìnÙ
o
, -t ( tL.3 'sfrttf I
ß-_ SrÌr
28.
z
L
A-=
\øt
s4.
10"
L,
.l .1 - +
.3'
- Z (q,t[z.3 )<or s
n- = IlZ.llolsqt
12
o- = lO,
S\
mlB =
mZC- lO,'lî'
8#=+
ry
.5T -- ¿c's A
29,
1r=zz+
-- 23
+
lôz
- z(z)(to) '
ent A
'
= - Z(¿Xp) cot A
E(
4-toe
D( - 1-'Cro
+
= êos A
--ccs¡
T--eosA @'-'
Two airplanss leave an airport, and the angle between their flight paths is 40o' An hour
later, onL plane has traveled 300 miles while the other has traveled 200 miles. How far
apart are the planes at this time?
g
X'- @ùt*(u)"- z(,þ)(::),
X' =
3 8074-çcctE
Name:
Geometry Quiz: TrÍgonometry
KeV
a-2
1. If sin Q =5 /r,then cos Q =
5'+X-
=7
24
xz/= zí
Solve for each variable.
\."ïlï;'i'**
dn Lt--ä
| = tz(sm u)
strt zs=
{= JE
sin 2€
I
z, ^= I .3Ö
3. x=
Y
3G.81
The equal sides of an isosceles triangle are23 inches long. If each base angle is 56
degrees, find the length of the altitude.
q
l1
5,
The grade of the rodd is lZ%o. Find the angle the road makes with the horizontal.
/.\--
t2-
lan e = IOO
loo
A water slide
e- 6;t ffi)
=
00 meters long and starts at the top of a tower that is 45 meters high, Find
the angle of elevation between the slide and the ground.
\5/\
is
/r
¿Jf
f,=
sfn
6
>--t-
!= sí,ì ' (Iã) =[78]
.ot
,^
7
.
x
Find the measures of the angles of a7-?L25 right triangle.
(= #
sr^
f
=
.Jr'h
-7e ,q
-' (!t)
=
-73 -J',{
2rl
8.
lG .
If
the diagonals of a rhombus have lcngths
of the angles of the rhombus.
of l2
meters and
lrt. zt'
',
za'
l6 meters,find the measures
&'' 8= *
D-nA
Q
=
(¡^-l
7'e '-
G) = sÇ.t7'
z-3c-87
<
1
loc
3 .-?1'
=^LA = ¡¿ C
za
mLD -^L
B
A jet takes off at a 4Oo angle. The jet's air speed is 300 feet per second.
a.
After 10 seconds what horizontal distance
Afte
the jet's
has the
jet traveled?
altitu
3
10.
From the top of a6?.Çfoot high bluff, a rescue scout looks down upon a hot-air balloon
accident, The angle of depression is 8o. How far is the accident from the rescue team at
the foot of the
blufflr
)1
-
Eoi
\l
n
\
\\
GZ'l
I
fartt = +
1 1 s1 ,11r