Question

question 9 multiple - choice worth 1 point a ramp into a building forms a 6° angle with the ground. if the ramp is 8 feet long, how far away from the building is the entry point of the ramp? round the solution to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ramp is the hypotenuse ($c = 8$ feet) and the distance from the building to the entry point of the ramp is the adjacent side to the given angle $\theta=6^{\circ}$. We use the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
Let $x$ be the distance from the building to the entry point of the ramp. Then $\cos\theta=\frac{x}{c}$.

Step2: Solve for $x$

We know that $\theta = 6^{\circ}$ and $c = 8$. Substitute into the formula: $x = c\cos\theta$.
$x=8\times\cos(6^{\circ})$.
Since $\cos(6^{\circ})\approx0.9945$, then $x = 8\times0.9945=7.956\approx7.96$ feet.

Answer:

$7.96$ feet