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:
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
For our problem:
[tex]\displaystyle \sin 20^\circ=\frac{H}{21.5}[/tex]
Solving for H:
[tex]H=21.5\cdot \sin 20^\circ[/tex]
Find the sine of 20° by using a calculator:
[tex]H=21.5\cdot 0.342[/tex]
H=7.35 feet
The porch is 7.35 feet off the ground
