Download Name - Mayfield City Schools

Math 2
Quiz Review: Lessons 5-1 & 5-2
Name _____________________________
Date ____________________________
I. Referring to the diagram, give the value of each trigonometric ratio.
1. sin  P   ________
Q
5. tan Q   ________
2. sin Q   ________
3
6. cos  P   ________
3. cos  P   ________
R
4
P
4. tan  P   ________
7. m  P ≈ __________
8. m  Q ≈ __________
II. Find the missing sides and angles. Round to the nearest 100th.
B
C
A
1. AB = 10, m B  43 Find CA.
2. AC = 18, m A  18 . Find BC.
3. AC = 23, m B  34 . Find AB.
4. BC = 12.6, BA = 18.8. Find mB and m C
Angle of Elevation/Depression
OBJECT
OBJECT
OVER 
Page 2
Right Triangle Word Problems
1.
2.
3.
4.
5.
Read the problem carefully.
Draw and label the triangle.
Set up the equation.
Solve the equation.
Answer the question.
1. A boy who is flying a kite lets out 300 feet of string which makes an angle of 52 with the ground.
Assuming that the string is stretched taut, find, to the nearest foot, how high the kite is above ground.
2. Find, to the nearest degree, the angle which the sun’s rays make with the ground when a flagpole 40
feet high casts a shadow 30 feet long.
3. An airplane rises at an angle of 14 with the ground. Find, to the nearest 10 feet, the distance it has
flown when it has covered a horizontal distance of 1500 feet.
Page 3
4. An isosceles triangle has sides length 5, 5, 6. Find the measure, to the nearest degree, of each base
angle of the triangle. (Hint: Draw the altitude from the vertex angle to the base.)
5. An observation tower is 75 m high. A support wire is attached to the tower 20 m from the top. If the
support wire and the ground form an angle of 46 degrees, what is the length of the support wire, to the
nearest tenth?
6. In an isosceles triangle the vertex angle measures 64 degrees and each leg measures 10 inches, find, to
the nearest tenth of an inch, the length of the altitude to the base.
7. A bird rises 20 meters vertically over a horizontal distance of 80 meters. What is the angle of
elevation? Round to the nearest degree.
OVER 
Page 4
8. How far below sea level, to the nearest meter, will a dolphin be if it swims 250 meters at a 12 angle
of depression?
9. At a point on the ground 40 feet from the foot of a tree, the angle of elevation of the top of the tree is
42 . Find the height of the tree, to the nearest tenth of a foot.
10. An observer in a balloon, which is 2000 feet above an airport, finds that the angle of depression of a
steamer ship out at sea is 21 degrees. Find, to the nearest hundred feet, the distance between the
observer in the balloon and the steamer ship at sea.
11. From a 200 feet high cliff a boat is noticed floundering at sea. The boat is approximately 300 yards
from the base of the cliff. What is the angle of depression, to the nearest degree, of the line of sight to
the boat?
12. Two students want to determine the heights of two buildings. They stand on the roof of the shorter
building. The students use a clinometer to measure the angle of elevation of the top of the taller
building. The angle is 44 o . From the same position, the students measure the angle of depression of the
base of the taller building. The angle is 53 o . The students then measure the horizontal distance
between the two buildings. The distance is 18.0 m. The students drew this diagram. How tall is each
building? Round to the nearest tenth.
Word Problem Answers:
7. 14
o
8. 52m
1. 236ft
9. 36.0ft
2. 53
o
3. 1550 ft
10. 5600ft
4. 53
11. 13
o
o
5. 76.5m
6.
8.5in
12. 23.9m & 41.3m