Question

A ramp into a building forms a 7° angle with the ground. If the entry point of the ramp is 6 feet from the building, how many feet long is the ramp? Round the solution to the nearest hundredth.

5.33 feet
6.05 feet
7.04 feet
7.96 feet

Answer 1

To find the length of the ramp, we can use the relationship between the angle, the height, and the length of the ramp in a right triangle.

Given:
- The angle (θ) = 7°
- The distance from the entry point of the ramp to the building (adjacent side) = 6 feet

We will use the cosine function, which is defined as:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

Here, the hypotenuse is the length of the ramp, which we will denote as \( L \). So we can rearrange this formula to solve for \( L \):

\[
L = \frac{\text{adjacent}}{\cos(\theta)}
\]

Substituting the known values:

\[
L = \frac{6}{\cos(7^\circ)}
\]

Now, we need to calculate \( \cos(7^\circ) \):

Using a calculator:
\[
\cos(7^\circ) \approx 0.992546
\]

Now, substituting this value into the formula for \( L \):

\[
L \approx \frac{6}{0.992546} \approx 6.04
\]

Rounding to the nearest hundredth gives 6.04 feet.

Among the options provided:
- 5.33 feet
- 6.05 feet
- 7.04 feet
- 7.96 feet

The closest option to our calculated value of 6.04 feet is **6.05 feet**.