Question

Find the angle. Round your answer to the nearest whole number.

Answer 1

Trigonometric Ratios

The trigonometric ratios are used on right triangles to relate angles and side lengths.

We are given the lengths of the three sides of the right triangle, so we can use any of the trigonometric ratios available. Let's choose, for example, the sine ratio, whose formula is:

`\displaystyle\sin \theta=\frac{\text{opposite leg}}{\text{hypotenuse}}`

We want to calculate the value of the angle marked as '?', called theta in the formula above.

Please note the opposite leg to the angle is 16 and the hypotenuse is 34, thus:

`\displaystyle\sin \theta=(16)/(34)=0.47059`

The angle is calculated as the inverse sine function:

`\theta=\arcsin (0.47059)=28.07^o`

Rounding to the nearest whole number:

Angle '?' = 28°