Question

Find the missing side. Round your answer to the nearest tenth.

Answer 1

x = 37.3 (nearest tenth)

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• θ is the angle.
• O is the side opposite the angle.
• A is the side adjacent the angle.
• H is the hypotenuse (the side opposite the right angle).

Given:

• θ = 40°
• O = 24
• H = x

Substitute the given values into the sine ratio and solve for x:

`\implies \sf \sin(40^(\circ))=(24)/(x)`

`\implies \sf x=(24)/(\sin(40^(\circ)))`

`\implies \sf x=37.33737184...`

`\implies \sf x=37.3\;(nearest\;tenth)`

Therefore, x = 37.3 (nearest tenth).