Question

Which of the following is the best estimate of the measure of the angle the skateboard makes with the ground ?

Answer 1

Correct choice: C. 74.5

Explanation:

Trigonometric Ratios

In every right triangle (those who have an internal angle of 90°), the six trigonometric ratios are valid. They relate the other internal angles with the lengths of the triangle.

The skateboard, the wall, and the ground form a right triangle. We need to find the measure of the angle formed by the skateboard with the ground. Let's call it β. In a right triangle, the cosine of an angle is defined as

`\displaystyle \cos\beta=\frac{\text{adjacent leg}}{\text{hypotenuse}}`

The adjacent leg of β is the side with length 8 in, and the hypotenuse is the length of the skateboard, 30 in, thus:

`\displaystyle \cos\beta=(8)/(30)}=0.267`

Using a digital calculator we find:

`\beta=\cos^(-1)(0.267)`

`\beta=74.5^\circ`

Correct choice: C. 74.5