Question

1. ramps a 60 - foot ramp rises from the first floor to the second floor of a parking garage. the ramp makes a 15° angle with the ground. how high above the first floor is the second floor? express your answer to the nearest tenth of a foot.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(15^\circ)=\frac{y}{60}$

Step3: Solve for height $y$

$y = 60\times\sin(15^\circ)$
Calculate $\sin(15^\circ)\approx0.2588$, so $y\approx60\times0.2588=15.528$

Step4: Round to nearest tenth

$y\approx15.5$

Answer:

15.5 feet