Question

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

Answer 1

Answer:

Correct choice: C. 74.5

Step-by-step 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:

$\displaystyle \cos\beta=\frac{8}{30}}=0.267$

Using a digital calculator we find:

$\beta=\cos^{-1}(0.267)$

$\beta=74.5^\circ$

Correct choice: C. 74.5