Final answer:
To find the maximum height of the skateboard ramp, we use the sine function with the given 20-degree angle of elevation and the ramp length of 34 inches to calculate the height, which is approximately 11.6 inches.
Step-by-step explanation:
To determine the height at which the skateboard ramp will rise from the ground at its highest end, we can use trigonometry. Specifically, we use the sine function since we have the hypotenuse (the length of the ramp, which is 34 inches) and we want to find the opposite side (the height) of the right triangle formed by the ramp and the ground. The angle of elevation is given as 20 degrees.
The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. Therefore:
sin(20°) = opposite / hypotenuse
sin(20°) = height / 34 inches
To solve for the height, we multiply both sides by 34 inches:
height = sin(20°) × 34 inches
Calculating this, we get:
height ≈ sin(20°) × 34 ≈ 0.342 × 34 inches ≈ 11.6 inches
Therefore, the ramp will rise approximately 11.6 inches off the ground at its highest end, which can be rounded to 11.6 to the nearest tenth of an inch.