Download Geometry 2(H): Trigonometry Name Unit Review Period Date

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Name ______________________________________
Geometry 2(H): Trigonometry
Unit Review
Period _______________ Date _________________
G.SRT.6 Learning Target: Understand that by
3) Given ABO KLJ . If the cos A = 0.6 and JK
similarity, side ratios in right triangles are properties of
= 4, what is the length of LK?
the angles in the triangle, leading to definitions of
trigonometric ratios for acute ratios.
1) Given the following trig ratios, what is the length
of AC?
A
C
36
B
12
13
5
cos A 
13
12
tan A 
5
sin A 
Answer: ___39_________
2). Complete the following trig ratios for
Answer:
____2.4__________
4) Darren started
with a 45-45-90
triangle ( HKI )
and then reflected it vertically to get a congruent
triangle, JKI . The length of HK is 5 cm.
ACB
sin A = 17/21 cos A = 10/21 tan A = 17/10
Then, Darren claimed the following:
- Since the two smaller triangles HIJ ,
using the triangle angle sum theorem,
HIJ is 90º
- Since HK is 5 cm, then JK and KI are
also 5 cm.
-
Using the Pythagorean Theorem, the length
of HI and JI is 5 2 .
-
The length of HJ is 10 cm.
5 2
2

The tan ( IHK ) =
10
2
-
The tan 45º =
2
2
Sadly, Darren went wrong somewhere in his
assumptions. Find his mistake and correct it.
____ His tangent ratio is wrong. It should be 1.
_______________________________________
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G.SRT.7 Learning Target: Explain and use the
G.SRT.8 Learning Target: Use trigonometric
relationship between the sine and cosine of
complementary angles.
ratios and the Pythagorean Theorem to solve right
triangles in applied problems
5. Given that two angles of a right triangle are
complementary, explain how to find the sine of one
angle, given the cosine of the complementary angle.
8) Which expression(s) can be used to find the value
of x in the triangle? There may be more than one.
The sine of one angle is equal to the cosine of its
complement.
6) In the right triangle ABC, A and B are
complementary angles. Which statement is TRUE?
C
20
48
A
B
52
a) The cos A and the sin B are both equal to
12
.
13
(a) x 
14
cos 59
(b) x  14cos59
sin 59
(c) x 
14
(d) x  14
sin 59
14
sin 31
b) The cos A= 12 and the sin B =
.
13
13
(e) x 
c) The cos A and the sin B are both equal to 5
13
5
12
d) The cos A=
and the sin B =
.
13
13
(f) x  14 tan 59
5
Answer: ___ C __________
Answer(s)__ A and E ____
9). How long is the guy wire shown in the
figure if it is attached to the top of a 50-ft
antenna and makes a 70° angle with the
ground? Round to the nearest
tenth.
7). What is the solution to the following
equation? If there is more than one solution,
would both work? Why or why not?
cos (x2 + 36)° = sin (4x + 9)°
Answer: __x = 5________
Explanation: x = -9 could not work, because an
angle can’t be negative
Answer: __53.2 ft _______
10). You are flying a kite!! The angle of depression
is 23º. If your eyes are five feet high, how high off
the ground is the kite? Round your answer to the
nearest tenth.
11) If the length of each side of the square sign
shown below is 15 inches, how long is the diagonal?
(Round to the nearest inch.)
Answer: ____21 inches ____________
12) A skateboard ramp has a slope of 2/5.
Part A: What is the angle of elevation for the ramp?
21.8°
Part B: A similar skateboard ramp is 20 feet long,
what is its vertical rise?
7.4 feet
Part C: What is the slope of this second ramp?
Answer: __24.5 m ______________
7.4
7

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