Question

Find the measure of side c. Triangle A B C has a right angle at angle C. The measure of angle A is 29 degrees. Hypotenuse A B is labeled "c" and leg B C is labeled "a = 33 meters." 29 o c a = 33 m

Answer 1

Given:

In triangle ABC, right angle at angle C.

$a = 33$ meters

$m\angle A=29^\circ$

To find:

The measure of side c.

Solution:

In a right angle triangle,

$\sin \theta =\dfrac{Perpendicular}{Hypotenuse}$

It is also written as:

$\sin \theta =\dfrac{Opposite}{Hypotenuse}$

In triangle ABC, angle C is a right angle. It means the side c is the hypotenuse.

In triangle ABC,

$\sin A=\dfrac{a}{c}$

$\sin 29^\circ=\dfrac{33}{c}$

$c=\dfrac{33}{\sin 29^\circ}$

On further simplification, we get

$c=\dfrac{33}{0.4848}$

$c=68.0693$

$c\approx 68.07$

Therefore, the measure of side c is 68.07 meters.