﻿ Trigonometric Ratios Worksheet | Problems & Solutions

# Trigonometric Ratios Worksheet

Trigonometric Ratios Worksheet
• Page 1
1.
The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft from the base of it. Fnd the height of the flag pole.
 a. 18 ft b. 12 ft c. 20 ft d. 22 ft

#### Solution:

Let x be the height of the flagpole.

tan 48° = x18

x = 18 tan 48°

x = 18 × (1.110612515) = 20

So, the height of the flag pole is 20 ft.

2.
In right triangle PQR, if $\angle$Q = 90°, $\angle$R = 22° and $q$ = 35, then the measure of $r$ to two significant digits is ____.

 a. 35 b. 15 c. 13 d. 32

#### Solution:

sin 22° = r35
[sin R = rq.]

r = 35 × sin 22° = 35 × (0.374606593)

= 13, to two significant digits.

3.
In right triangle ABC, if $\angle$B = 90°, $\angle$C = 70° and $c$ = 18, then the measure of $b$ to two significant digits is:

 a. 16 b. 19 c. 18 d. 29

#### Solution:

Sin 70° = 18b
[sin C = cb.]

b = 18sin70o

b = 18 csc 70°

= 18 (1.064177772) = 19, to two significant digits.

4.
In right triangle DEF if $\angle$D = 42°, $\angle$E = 90° and $f$ = 32, then the measure of $e$ to two significant digits is:

 a. 43 b. 21 c. 24 d. 29

#### Solution:

cos 42° = 32e
[cos D = fe.]

e = 32cos 42°

e = 32 sec 42°

= 32 × 1.34563273 = 43, to two significant digits.

5.
In right triangle PQR if $\angle$Q = 90°, $\angle$R = 30° and $r$ = 12, then the measure of $p$ to two significant digits is:

 a. 12 b. 21 c. 11 d. 24

#### Solution:

cot 30° = p12
[cot R = pr.]

p = 12 cot 30°

p = 12 × 1.732050808 = 21, to two significant digits.

6.
In an isosceles triangle ABC, if $b$ = 18, $c$ = 18 and $\angle$C = 50°, then the length (to two significant digits) of side $a$ is:

 a. 43 b. 27 c. 23 d. 30

#### Solution:

The altitude from A to BC divides the triangle into two congruent right triangles.

In right triangle ADC, DC = 12(a).

Cos 50° = a218 = a36
[cos C = DC / AC.]

a = 36 Cos 50° = 36(0.642787609) = 23, to two significant digits.

7.
In an isosceles triangle ABC, if $b$ = 20, $c$ = 20 and $\angle$C = 70°, then the length (to two significant digits) of the altitude drawn from A to BC is:

 a. 18 b. 15 c. 19 d. 23

#### Solution:

The altitude from A to BC divides the triangle into two congruent right triangles.

AD = 20 × sin 70° = 20 × (0.93969262)

AD = 19, to two significant digits.

8.
In right triangle ABC if $\angle$C = 90°, $\angle$B = 28°20′, and $b$ = 11.8, then the length of $c$ to three significant digits is:
 a. 11.8 b. 20.7 c. 24.9 d. 13.4

#### Solution:

sin 28°20′ = bc
[sin B = AC / AB.]

sin 28°20′ = 11.8c

c = 11.8sin28o20'

c = 24.86302319 = 24.9, to three significant digits.

9.
Find the value of sin A, if $x$ = 5 units, $y$ = 12 units and $a$ = 13 units.

 a. $\frac{12}{13}$ b. $\frac{13}{12}$ c. $\frac{5}{13}$ d. $\frac{13}{5}$

D is a point on side BC of ΔABC such that $m$$\angle$ADC = $m$$\angle$BAC. If CA = 10 cm. and CB = 15 cm, then what is the length of $\stackrel{‾}{\mathrm{CD}}$?