Study Island – Geometry: Circles and Right Triangle Trig
Copyright © 2014 Edmentum - All rights reserved.
1.
If
= 39° and m = 51 cm, what is the value of n to the nearest tenth of a centimeter?
A. 32.1 cm
B. 81 cm
C. 41.3 cm
D. 39.6 cm
2. Angles A and B are complementary angles in a right triangle. The value of sin(A) is
cos(A)?
A.
B.
C.
D.
. What is the value of
3.
Picture is not drawn to scale.
Howard is standing 86 yards from the bottom of a water reservoir. He estimates that the angle of elevation to
the top of the water reservoir is about 60°. How far is Howard from the top of the water reservoir?
A. 99 yards
B. 43 yards
C. 50 yards
D. 172 yards
4. Jaime is playing disc golf. He is standing across a creek from the basket at a 60° angle.
Note: picture not drawn to scale
Which equation can be used to find the distance, r, between him and the basket if he were to walk 5 more
meters?
A.
B.
C.
D.
5. If m
= 72°, what is the value of x?
*Image not drawn to scale
A. 18°
B. 36°
C. 12°
D. 6°
6.
The circle above has an area of 144
A. 150.72 cm2
B. 25.12 cm2
cm2. What is the area of the blue sector? Use 3.14 for
C. 113.04 cm2
D. 48 cm2
7. Which of the following functions is equal to cos(73°)?
A. sin(73°)
B. sec(17°)
C. sec(73°)
D. sin(17°)
.
8. Nicole is playing a baseball game on her computer. Her player is on second base. The distance on the screen
from third base to the pitcher's mound is 9 cm. The angle at second base is 55°, as shown in the figure below.
Note: picture not drawn to scale
Which equation can be used to find the length, r, between second and third base on the screen?
A.
B.
C.
D.
9. If m
= 288°, what is the value of x?
*Image not drawn to scale
A. 288°
B. 72°
C. 36°
D. 144°
10.
In the circle above, RV and SW are chords which intersect at point T.
If ST = 4 ft, TV = 8 ft, and TW = 12 ft, what is the length of RT?
A. 10 ft
B. 6 ft
C. 8 ft
D. 5 ft
11. If m
= 28°, what is the measure of
AEB?
*Image not drawn to scale
A. 7°
B. 42°
C. 14°
D. 28°
12. The measure of ABC is 120°. The length of radius BA is 8 centimeters. What is the area of the shaded,
larger sector? Use 3.14 for .
Note: Picture not drawn to scale.
A. 267.95 cm
B. 33.49 cm2
2
C. 133.97 cm2
D. 16.75 cm2
13. Which of the following functions is equal to sin(7°)?
A. cos(7°)
B. csc(83°)
C. csc(7°)
D. cos(83°)
14.
In the figure above, line AG is tangent to circle C at point F, the measure of
If the measure of
A. 72°
B. 25°
C. 38°
D. 11°
= 68°, what is m
GFE?
BFA = 61°, and
= 26°.
15.
Given: AC is a diameter, and point B is any point on
Prove:
.
ABC is a right triangle.
Proof:
Statements
Reasons
1. AC is a diameter
1. Given
2. m
2.
= 180°
3. m B = 90°
3. Measure of an inscribed angle
4. ABC is a right triangle.
4. Definition of a right triangle
Which reason completes the proof?
A. Intercepted arc theorem
B. Pythagorean theorem
C. Definition of a semicircle
D. Definition of a diameter
16.
Picture is not drawn to scale.
Mr. Jameson is walking toward his nine-story hotel and stops to look up to the top of the building. The angle of
elevation to the top of the hotel is 45°. If the height of the hotel is 90 feet, how far away is Mr. Jameson from
the hotel?
A. 127 feet
B. 141 feet
C. 90 feet
D. 129 feet
17.
Daniel sees a lighthouse in the harbor. He estimates the angle of elevation is 60°. If the lighthouse is 100 feet
tall, what is the approximate distance between Daniel and the top of the lighthouse? (Assume the lighthouse
meets the ground at a right angle.)
A. 87 feet
B. 200 feet
C. 58 feet
D. 115 feet
18. Which of the following functions is equal to sin(90° A. csc( )
B. cos( )
C. cot(90° -
)
D. csc(90° -
)
)?