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
[tex]\displaystyle \cos\beta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
The adjacent leg of β is the side with length 8 in, and the hypotenuse is the length of the skateboard, 30 in, thus:
[tex]\displaystyle \cos\beta=\frac{8}{30}}=0.267[/tex]
Using a digital calculator we find:
[tex]\beta=\cos^{-1}(0.267)[/tex]
[tex]\beta=74.5^\circ[/tex]
Correct choice: C. 74.5
