Download unit 10 review key

station l: pgthagorean Theorem
and Rationalizing Denominators
= ladder 25 feet long is
leaning against a wall 20 feet up the wall. How far is the bottom of the
ladder from the
hm of the wall?
1. Draw it
2. Show all work to support your answer
-z 20 2 4 X
. In the accompanying diagram of right triangles ABDand DBC,AB 5, AD 4, and CD— l. Find the length of BC,
leave answer in simplest radical form.
Write the following expression so that each denominator is a rational number. Simplify completely.
station L: SOHCAHTOA- CALCVLAIOR in
Which ratio represents the cosine of angle A in the right triangle below?
1)
3
4) 4
In triangle MCT,the measure of Z T = 900, MC = 85 em, CT= 84 em, and Tl'f= 13em. Which ratio represents
Hint: DRAW IT!)
85
84
85
84
13
The diagram below shows right triangle LMP.
Which ratio represents the angent of Z PIM?
Which equation shows a correct trigonometric ratio for angle A in the right triangle below?
sinA
tanA
—
17 cm
15 cm
sine
Complete both Column A AND Column B:
ColumnA
for the value of x, to the nearest tenth.
16
Column B
4. Solve for the nt4B to the nearest hundredth of a
degree
c
.4
x
IC
co c
;'
((0s9)
27
16
2. You go to the park on a windy day to fly a kite. You
have released 40 feet of string. The string makes an
angle of 360 with the ground. How high is the kite in the
air to the nearest foot?
5. A ladder is resting against le
eo a 111Ing. The
bottom of the ladder is 12 feet from the building, and
the ladder reaches 7 feet up the side of the building.
Find the measure of the angle of elevation, to the
nearest tenth of a degree. -1
HO
K
qosin(3G)
30t3
ee casts a 25-foot shadow on a sunny day, as
shown in the diagram below
6. The diagram below shows the path a bird flies from
the top of a 9.5 foot tall sunflower to a point on the
ground 5 feet from the base of the sunflower.
s
O
5
Ifthe angle of elevation from the tip of the shadow to
the top of the tree is 320, what is the height of the tree to To Re nearest tenth of a degree what is the measure of
angle x?
he nearest tenth of a foot?
us
ts,can
•••t Whaes the difference between problems in column A vs. Coltillkll B?
In
A,
In
6)
are
muse use
sides ðPftghÏ
ðPriQvt A's
stat ion 3: cofvnctbns
Solve the following problems using your knowledge of cofunctions:
eos 10 0
3. Ifsin6d=
cos 9.0 then m<A is equal to:
qooJ
zoo
5-1
2
4.
Which ',illue of-v satisfies the equation
= eos(.lx
sin(3x +
30
3) 12
= sin 550. lind the value of x.
5.
2K -R Csss
= 80
2K +30
6. The degree measure of an ang e In a right triangle is x, and sin x
= -. Which of the following
equal to 2.
3
valves
cos x
_Ä?os (x -90)
3) cos (90-x)
in(90
sink —
cos( 010-Äò = L
are also
station L}: exact
valves
Set up your Reference Materials 1st!
Draw the two special right triangles:
45-45-90
30-60-90
30
***IMPORTANT!You will not be GIVENthese values on the test. You have to memorize each EXACTvalue
for each angle!
2. Determine the exact trigonometric values for the follo ing:
cos30
b) sin 45
4. Using exact trig values, solve for y.
gntøn 5 1ŸigIdentifies
s;n29
I
Simplify Each Expression:
1)
1 — cos 2 0
2) tan O cos O
sin
sinÙ
tan Ocos O
sino
3)
set
sins
)
hic-I
O)
station G:Avxllnrg Lines
a) Given triangle DEF, ZD = 22 0, zF = 91 0,
- 16.55, and EF = 6.74, find DE to the nearest
hundredt
16 55
91 •
74
IIS cos(n)
CBs
O
ßOvf\/D
Ive for the area of triangle DEF. (Hint: You need the altitu e .
£ -
NQ-2ð
h
B)
(nqò(
A=5C
2. Given the following diagram, solve forAB to the nearest meter. (Hint: Draw altitude extending rot
S)hl)-- iso
bowsAl = x
C,
qî,gsù31Ä = x
H 01
station Jumbled Jamboree
1. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet
short
above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 70. A
Ab
time later, at point D, the angle of elevation was 160.
70
160
125 ft
c
tanlG
--HBSAÀOSS
2. The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is
composed of a hemisphere, a cylinder, and a cone. Let C' be the center of the hemisphere and let D be the center
of the base of the cone.
25
c:
8.5
If AC—8.5 feet, BF = 25 feet, and mLEFD = 470, determine the height of the water tower (from A to E) to the
nearest whole number.