Question

Use trigonometry to find the missing side. Round your answer to the nearest tenth (one decimal place)

Answer 1

Given:

A figure of a right triangle.

To find:

The missing side by using the trigonometric ratios.

Solution:

In a right angle triangle,

$\cos \theta=\dfrac{Adjacent}{Hypotenuse}$

In triangle ABC,

$\cos A=\dfrac{AC}{AB}$

$\cos (31^\circ)=\dfrac{b}{270}$

$0.857=\dfrac{b}{270}$

Multiply both sides by 270.

$0.857\times 270=b$

$231.39=b$

$b\approx 231.4$

Therefore, the missing side length is b=231.4 inches.