Download Geometry 2: Trigonometry Unit Review

Geometry 2: Trigonometry
Unit Review
Name ______________________________________
G.SRT.6 Learning Target: Understand that by
similarity, side ratios in right triangles are properties of
the angles in the triangle, leading to definitions of
trigonometric ratios for acute ratios.
Period _______________ Date _________________
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.
1) Given the following trig ratios, what is the length
of AC?
A
C
36
12
13
5
cos A 
13
12
tan A 
5
sin A 
B
Answer: ______________
2). Complete the following trig ratios for
ACB
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 .
sin A =
cos A =
tan A =
3) Given ABO KLJ . If the cos A = 0.6 and JK
= 4, what is the length of LK?
-
The length of HJ is 10 cm.
5 2
2
The tan ( IHK ) =

10
2
2
The tan 45º =
2
Sadly, Darren went wrong somewhere in his
assumptions. Find his mistake and correct it.
Answer:
______________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
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.
__________________________________________
__________________________________________
__________________________________________
_______________________________________
6) In the right triangle ABC, A and B are
complementary angles. Which statement is TRUE?
(a) x 
C
20
48
A
B
52
a) The cos A and the sin B are both equal to
12 .
13
5
b) The cos A= 12 and the sin B =
.
13
13
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
Answer: ______________
14
cos 59
(b) x  14cos59
sin 59
(c) x 
14
(d) x  14
sin 59
(e) x 
14
sin 31
(f) x  14 tan 59
Answer(s)______________
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? Round your answer to the nearest
tenth.
cos (2x + 18)° = sin (4x + 5)°
Answer: ______________
Answer: ______________
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.
Answer: ________________
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: ________________