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DIY Skateboard Ramp: Calculating Height & Base Length

Learn how to build a skateboard ramp using trigonometry. Calculate the height and base length for a 14-ft ramp with a 26° angle of elevation. Discover step-by-step solutions through sine and cosine ratios.

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DIY Skateboard Ramp: Calculating Height & Base Length

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  1. SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp. EXAMPLE 5 Find leg lengths using an angle of elevation

  2. Find the height. STEP 1 sin26o = x = opp. hyp. sin26o 14 14 sin 26o = x 6.1 x ANSWER The height is about 6.1 feet. EXAMPLE 5 Find leg lengths using an angle of elevation SOLUTION Write ratio for sine of 26o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  3. cos26o = cos26o y = adj. hyp. 14 14 cos 26o = y 12.6 y ANSWER The length of the base is about 12.6 feet. EXAMPLE 5 Find leg lengths using an angle of elevation Find the length of the base. STEP 2 Write ratio for cosine of 26o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  4. 3 3 Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, , and 2. Then set up sine and cosine ratios for the 60oangle. adj. hyp. opp. hyp. sin60o = 0.08660 = 2 1 cos60o = = 0.5000 = 2 EXAMPLE 6 Use a special right triangle to find a sine and cosine Use a special right triangle to find the sine and cosine of a 60o angle. SOLUTION

  5. WHAT IF? In Example 5, suppose the angle of elevation is 35o. What is the new height and base length of the ramp? ANSWER about 8 feet, about 11.5 ft 8. Use a special right triangle to find the sine and cosine of a 30o angle. 3 , ANSWER 2 1 2 for Examples 5 and 6 GUIDED PRACTICE 7.

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