The builder of a parking garage wants to build a ramp at an angle of $13^{\circ}$ that covers a horizontal span of 50 feet. How long will the actual ramp be? Round your solution to four decimal places.
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Final Answer: The length of the ramp will be approximately \(\boxed{11.5434}\) feet.
Step 1 ：This is a trigonometry problem. We can use the tangent of the angle to find the length of the ramp. The tangent of an angle in a right triangle is the ratio of the opposite side (the length of the ramp in this case) to the adjacent side (the horizontal span).
Step 2 ：So, we can set up the equation \( \tan(13) = \frac{length}{50} \) and solve for length.
Step 3 ：Substituting the given values into the equation, we get \( \tan(13) = \frac{length}{50} \).
Step 4 ：Solving for length, we get \( length = 50 \cdot \tan(13) \approx 11.543409556278156 \).
Step 5 ：Final Answer: The length of the ramp will be approximately \(\boxed{11.5434}\) feet.
