Download Trigonometry Word Problems For each problem, draw a picture an

Scholarship Algebra II
Trigonometry Word Problems
Name ____________________________________
For each problem, draw a picture and solve on a separate sheet of paper. Use the Pythagorean theorem,
SOHCAHTOA, Law of Sines, and/or Law of Cosines.
1. A 32-foot ladder leans against the side of a building and makes an angle of 75° with the ground. How
high above the ground is the top of the ladder? {30.9 ft}
2. How far apart are the outer ends of the hour and minute hands of a clock at two o’clock if the hour hand
is 8 cm long and the minute hand is 15 cm long? {13 cm}
3. Find the area of a regular 20 sided polygon inscribed in a circle of radius 12 cm. {445 cm2}
4. The angle of elevation from an observer on the ground to an airplane flying at an altitude of 8.3 km is
22.5°. How far is the observer in a straight line from the plane? {21.7 km}
5. Two ships leave from the same point at the same time on courses 33° apart at speeds of 12 km/h and 17
km/h respectively. How are far apart are the ships after 1 hour? {9.5 km}
6. One side of a parallelogram is 40 cm long. An adjacent side of length 22 cm makes an angle of 46° with
one of the diagonals of the parallelogram. Find the length of this diagonal. {52.0 cm}
7. The angle of depression from a ship to a wreck on the ocean floor is 10.9°. If the depth of the ocean at
the wreck is 156 m, how far should the ship sail so that it is directly over the wreck? {810.1 m}
8. Two adjacent sides of a parallelogram form an acute angle and have lengths of 25 cm and 32 cm. If the
shorter diagonal of the parallelogram has length 10 cm, what is the measure of the acute angle between
the sides? {14.5°}
9. Two observers on the ground, who are 15 km apart, spot a plane overhead. The angles of elevation of
the observers’ lines of sight are 49.8° and 60.5°, respectively. (The plane is in between the two
observers.) How far is the plane from the second observer at this moment? {12.2 km}
10. A baseball “diamond” is actually a square 90 feet on each side. The pitcher’s mound is 60.5 feet from
home plate. How far is the pitcher’s mound from first base? (Caution: Is the pitcher’s mound in the
exact middle of the square?) {63.7 ft}
11. Find the area of a regular pentagon with a side length of 10 cm. {172.0 cm2}
12. Find the area of a regular decagon (10 sides) with an apothem of 8 cm. (The apothem is a segment from
the center of a regular polygon to the middle of one of its sides.) {208 cm2}
13. Sketch a 30-60-90 right triangle and label the sides using the ratios you learned in geometry. Then find
the exact values (in radical form – no decimals!) of sin 30°, cos 30°, tan 30°, sin 60°, cos 60°, and tan
60°.
14. Sketch a 45-45-90 right triangle and label the sides. Find the exact values of sin 45°, cos 45°, and tan
45°.