Question

wheelchair ramp forms 20° angle with the ground. If the length of the ramp to the porch is 21.5 feet, how high (H) off the ground is the porch?

Answer 1

Answer:

The porch is 7.35 feet off the ground

Step-by-step explanation:

Trigonometric Ratios

The ramp, the height of the porch, and the distance from the base of both form a right triangle where trigonometric ratios can be applied.

The angle of 20° has the height of the porch H as the opposite side, and the hypotenuse is the length of the ramp.

The sine is defined as:

$\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}$

For our problem:

$\displaystyle \sin 20^\circ=\frac{H}{21.5}$

Solving for H:

$H=21.5\cdot \sin 20^\circ$

Find the sine of 20° by using a calculator:

$H=21.5\cdot 0.342$

H=7.35 feet

The porch is 7.35 feet off the ground