Download 5~52 y

Trigonometry review - SOHCAHTOA, Law of Sines and Law of Cosines
Show all work with the formulas. When an exact answer cannot be found, round your final answer to 2 decimal places.
1. Find the missing sides.
3. Find LY and the area of the triangle ..
5~52
2
.
~~
y
75.4
mLY = 45
L
°
mLL = 120
z
s
y
20
mLY=
12.3
Draw the following triangle to scale and find mLB and LC. If there are two triangl~s, find both.
5. mLA
=55 °, a= 5 em, b = 6 em
mLB= _ _ _ _ __
mLC= _ _ _ _ __
If 2 L\s, fill this out too. If there's
only 1 L\, cross this out.
mLB= _ _ _ _ __
mLC= _ _ _ _ __
A
6. For the triangle shown, give the range of values for side a that would result in.
/=:\
A
B
7. Hans sees a Pyramid and wonders how tall it is .. The angle of elevation to the top is 22.2
new angle of elevation is 15.7
°.
b) no triangle __ < a < _
a) two triangles _ _ < a <
Hans' eyes are 5.5 feet high. How tall is the Pyramid?
...
...
.
.
.
....
.....
...
....
.
...•..•....•...•.....••..
~
°.
When he walks 300 feet away, the
8.
6 YES has mLY = 45 °, YE =52 and YS = 60.
9. Find mLX if in
11 STX, mLS = 42 °,
s= 53.4 and x= 12.
Find the measure of LE (Include a diagram)
10.
Surveying Property A surveyor locating the comers of a triangular piece of property started at one comer and walked
480 ft in the direction ofN36°W to reach the next comer. Th"i:
surveyor turned and walked S21 ow to get to the next comer o••
the property. Finally, the surveyor walked in the direction
N82°E to get back to the starting point. What is the area ofth(}
property in square feet?
11.
Adjacent Pipes An engineer wants to position three pipes at
the ver!lces of a triangle, as shown in the figure. If the pipes A,
B, and C have radii 2 in., 3 in., and 4 in., respectively, then
what are the measures of the angles of the triangle ABC?
12. How many triangles are possible for each situation? Justify your answer.
a) mLA = 20.5
a= 12
b = 31
°
b) mLC
= 110 °
a= 20
c = 15.2
13. From a fire tower SO meters high, the angles of depression of two fires, which are on a horizontal line through the base of the
tower, are 1'45' and 3'. How far apart are the fires, if they are on the same side of the tower?
Trigonometry review - SOHCAHTOA, Law of Sines and Law of Cosines
Show all work with the formulas. When an exact answer cannot be found, round your final answer to 2 decimal places.
3. Find LV and the area of the triangle ..
1. Find the missing sides.
L
m.LY = 45"
X
12.3
" - l(
LF1 - -
f/)..J;
5. m.LA =55 °, a= 5 em, b = 6 em
11.4/
m.LB=
m.LC =
6
_Lf_<:;_,_)_~~
if 2 Lis, fill this out too. If there's
only 1 Ll, cross this out.
tOO~~~
m.LB =
m.LC
1
=
d-- ~ ' ~I
0
0
'\tt,i\
A
.· ~, '\
0
?. -~~ ~
b) no triangle __ <-.a < _
new angle of elevation is 15.7
°.
Hans' eyes are 5.5 feet high. How tall is the Pyramid?
ii)'". I
s~
', ,r,
...
.
·h ··....
.
. ..•.•...••....•...•..•
. -lst -.. .
~~~~~~-:~·
~
x
~. . / \ f ( " ' " '
-:~•. I (p,.)
;;;--3 6'1)
Y. ~~ '1' \ ?-
11v ~ rorNJ
rt~.Ll~r~
+vJ}
1
f+S S ,
8.
6 YES has mLY = 45 °, YE =52 and
1
~tt~o.'
9. Find mLX if in
b. STX, mLS = 42 °,
s= 53.4 and x= 12.
Find the measure of LE (Include a diagram)
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. ',
i
coS.
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uo
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~l~
1
(Y L\ ':> • L\ ~ _ s,~)
c..oS
'·"" ~ ~ St? ~ +-
::..
UIU
!LC
s;jh•-L-:\-i<-~
S'--~-!b.
s·. vi tt ~ , s.
~c.~. £ ~rv'•t.\W- ~
~ • !"'01. c.o s. £
'-'
do~
I
10. Surveying Property
urveyor ocatmg the comers of a tri~
angular piece of property started at one corner and walked
480ft in the direction ofN36°W to reach the next comer. The·
surveyor turned and walked S21 ow to get to the next comer o"
th~operty. Finally, the surveyor walked in the direction
.
N@_VE to get back to the starting point. hat is the area of the'
property in square feet?
11.
53. '-{
X-- 00.
>/',
-x
I d-
l~;;t>Y'·~.'
/d{iL~i~~ rt:f:/.\ 11· ')
los
0
~
Adjacent Pipes An engineer wants to position three pipes at
the vertices of a triangle, as shown in the figure. If the pipes A,
B, and C have radii 2 in., 3 in., and 4 in., respectively, then
what are the measures of the angles of the triangle ABC?
$'\n~- Si""· '~l
c.... - ~.~
c.... -;:. 4 ~cs.·(,., $"~
S'•n (sd
-~·
c., ~~~~0----?-7.;
I
~~-~-·- ·-~
.
~~ ~ .~~..o-=
YL/.Y~~
A
G
s-"· '~= B
13. From a fire tower 50 meters high, the angles of depression of two fires, which are on a horizontal line through the base of the
tower, are 1'Wnd 3'. How far apart are the fires, if they are on the same side of the tower?