The problem is to find the horizontal width of a skateboard ramp given the height and angle of incline.**Problem**: Find the horizontal width of a skateboard ramp if it has a height of 3 feet and a 20-degree incline. Round your answer to the nearest hundredth of a foot.**Solution**:To solve this problem, you can use trigonometry, specifically the tangent function in a right triangle, which relates the angle to the opposite side and adjacent side.Let's denote:- The height of the ramp (the vertical side of the right triangle) as $ h = 3 $ ft.- The angle of the ramp incline as $ \theta = 20^\circ $.- The horizontal width (the length of the adjacent side to the angle), which we need to find, as $ w $.Using the tangent function:\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]\[ \tan(20^\circ) = \frac{3}{w} \]Solving for $ w $:\[ w = \frac{3}{\tan(20^\circ)} \]Using a calculator to find $ \tan(20^\circ) \approx 0.364 $:\[ w \approx \frac{3}{0.364} \]\[ w \approx 8.24 \]Hence, the horizontal width of the ramp is approximately 8.24 feet.

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Answered: Find the horizontal width of a…

Find the horizontal width of a skateboard ramp if it has height 3 ft and a 20-degree incline. Round your answer to the nearest hundredth of a foot.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

The problem is to find the horizontal width of a skateboard ramp given the height and angle of incline.

**Problem**:
Find the horizontal width of a skateboard ramp if it has a height of 3 feet and a 20-degree incline. Round your answer to the nearest hundredth of a foot.

**Solution**:
To solve this problem, you can use trigonometry, specifically the tangent function in a right triangle, which relates the angle to the opposite side and adjacent side.

Let's denote:
- The height of the ramp (the vertical side of the right triangle) as $ h = 3 $ ft.
- The angle of the ramp incline as $ \theta = 20^\circ $.
- The horizontal width (the length of the adjacent side to the angle), which we need to find, as $ w $.

Using the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
\[ \tan(20^\circ) = \frac{3}{w} \]

Solving for $ w $:
\[ w = \frac{3}{\tan(20^\circ)} \]

Using a calculator to find $ \tan(20^\circ) \approx 0.364 $:

\[ w \approx \frac{3}{0.364} \]
\[ w \approx 8.24 \]

Hence, the horizontal width of the ramp is approximately 8.24 feet.

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