Question

What is the angle θ in the triangle below? (Hint: Use an inverse trigonometric function.)

A. 45.3°
B. 22.0°
C. 68.0°
D. 0.38°

Answer 1

The correct answer is B

Step-by-step explanation

The side length opposite to the angle
`\theta` has length
`3` units.

The length of the hypotenuse is
`8` units.

We use the trigonometric ratio that involves the length of the opposite side and the hypotenuse, which is

`\sin\theta=(Opposite)/(Hypotenuse)`

`\sin\theta=(3)/(8)`

This is the same as,

`\sin\theta=0.375`

We take the sine inverse to obtain,

`\theta=\sin^(-1)(0.375)`

This evaluates to

`\theta=22.024`

Therefore the value of the angle
`\theta` is
`22.0\degree` to the nearest tenth