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.
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