Question

1. Replace the ? with the correct value and solve the equations for the missing sides.

A
Find C
C
sin 22
b
=
118⁰
sin (?)
24
a
24
22°
B
sin (118)=
a=
b=
a
sin (7)
24

Answer 1

The measure of angle C is determined as 40⁰.

The value of side a is determined as 32.97.

The value of side b is determined as 13.97.

How to calculate the value of the missing angles and side lengths?

The value of angle C is calculated by applying sine rule as follows;

sin (118) / a = sin (C) / 24

The measure of angle C is calculated as follows;

A + B + C = 180 (sum of angles in a triangle)

118 + 22 + C = 180

140 + C = 180

C = 180 - 140

C = 40⁰

The value of side a is calculated as;

sin (118) / a = sin (40) / 24

a = (sin 118 / sin 40) x 24

a = 32.97

The value of side b is calculated as;

sin (22) / b = sin (40) / 24

b = (sin 22 / sin 40) x 24

b = 13.97