High School

Tamika wants to use a sheet of fiberboard 19 inches long to create a skateboard ramp with a 20-degree 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 if necessary.

A. 6.5 inches
B. 6.8 inches
C. 6.2 inches
D. 7.1 inches

Answer :

Final answer:

The ramp will rise 6.5 inches above the ground at its highest end, calculated using the sine function in trigonometry.

Explanation:

Tamika wants to determine the height at which a skateboard ramp will rise from the ground given a 19-inch long fiberboard sheet and a 20-degree angle of elevation. To calculate this, you can use the sine function from trigonometry, which is defined as the opposite side over the hypotenuse in a right-angled triangle. The formula would be:

height (= opposite side) = hypotenuse * sin(θ)

  1. Here, the hypotenuse is 19 inches, and θ (theta) is the 20-degree angle.
  2. Thus, height = 19 * sin(20°).
  3. Calculating this gives approximately 6.5 inches, which corresponds to answer choice (a).


Therefore, the ramp will rise 6.5 inches above the ground at its highest end.

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