﻿ Application of Trigonometric Functions Worksheet | Problems & Solutions

# Application of Trigonometric Functions Worksheet

Application of Trigonometric Functions Worksheet
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1.
Two boys are standing on either side of a pole that is $h$ = 170 m long. Their angles of elevation of the top of the pole measures 30°20′ and 45°30′. Find the distance between the two boys. (The position of the boys and the foot of the pole are collinear.)
 a. 291 m b. 458 m c. 124 m d. 167 m

2.
A flagpole is placed on top of the building. From a point on the ground $d$ = 250 ft from the base of a building, the angles of elevation of the top and bottom of the flagpole are 70°15′ and 57°20′. Find the height of the flagpole.
 a. 306 ft b. 390 ft c. 1086 ft d. 696 ft

3.
A pillar of height 226 ft casts a shadow of 360 ft long. Find the measure of the angle of elevation of the sun.
 a. 58° b. 51° c. 32° d. 39°

4.
An airplane is flying at an altitude of 1150 m. From the plane the angle of depression of a tree on the ground is measured as 15°. What is the distance from the plane to the tree?
 a. 4443 m b. 1150 m c. 1191 m d. 4292 m

5.
The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft away from its base. Find the height of the flagpole approximately.
 a. 16 ft b. 12 ft c. 27 ft d. 20 ft

6.
In right triangle ABC if $\angle$C = 90°, $\angle$B = 28° 20′, and $b$ = 16.5, then find the length of $c$.
 a. 7.8 b. 30.6 c. 18.7 d. 34.8

7.
In an isosceles triangle STV if $s$ = 18, $v$ = 18 and $t$ = 30, then find the measure of $\angle$STV to the nearest degree.

 a. 68° b. 56° c. 112° d. 146°

8.
In right triangle PQR if $\angle$Q = 90°, $\angle$R = 30° and $r$ = 27, then find the measure of $p$ to two significant digits.

 a. 47 b. 13 c. 16 d. 23

9.
In right triangle DEF if $\angle$D = 42°, $\angle$E = 90° and $f$ = 27, then find the measure of $e$ to two significant digits.

 a. 11 b. 18 c. 36 d. 27

In right triangle PQR, if $\angle$Q = 90°, $\angle$P = 42°10′ and $q$ = 24.3, then find the length of $r$.