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Tamika wants to use a sheet of fiberboard 19 inches long to create a skateboard ramp with a
20^(@) angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch ifnecessary.

Tamika wants to use a sheet of fiberboard $19$ inches long to create a skateboard ramp with a $20^{\circ}$ angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch ifnecessary.

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Pythagorean theorem

Full solution

Q. Tamika wants to use a sheet of fiberboard

19

inches long to create a skateboard ramp with a

20^{\circ}

angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch ifnecessary.

Question Prompt: question_prompt: How high will the ramp rise from the ground at its highest end?
Identify Function: Identify the trigonometric function to use. Since we have the angle and the length of the ramp, which is the hypotenuse, and we want to find the height, which is the opposite side, we use the sine function.
Write Sine Function: Write down the sine function for the angle given. $\sin(20^\circ) = \frac{\text{opposite}}{\text{hypotenuse}}$ .
Plug in Values: Plug in the values we know into the sine function. $\sin(20^\circ) = \frac{\text{height}}{19}$ inches.
Solve for Height: Solve for the height. $height = 19 \, \text{inches} \times \sin(20^\circ)$ .
Calculate Height: Calculate the height using a calculator. $height = 19 \times \sin(20°) \approx 19 \times 0.3420 \approx 6.498$ inches.
Round Answer: Round the answer to the nearest tenth of an inch. height $\approx 6.5$ inches.

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