Question

The bottom of a doorway to a building is 3.45 feet above the ground, and a ramp to the door for the disabled is at an angle of 6 degrees with the ground. How much longer must the ramp be in order to make the angle 3 degrees? Round the answer to the nearest tenth.

Answer 1

Answer:

The ramp should be 32.9 feet longer.

Step-by-step explanation:

When the ramp is at $6^{o}$ to the ground, its length can be determined by applying the appropriate trigonometric function. Let the length be represented by l, so that;

Sin θ = $\frac{opposite}{hypotenuse}$

Sin $6^{o}$ = $\frac{3.45}{l}$

l = $\frac{3.45}{Sin 6^{o} }$

 = $\frac{3.45}{0.10453}$

 = 33.0048

l = 33.0 feet

When the angle is reduced to $3^{o}$, the length of the ramp would be;

Sin θ = $\frac{opposite}{hypotenuse}$

Sin $3^{o}$ = $\frac{3.45}{l}$

l = $\frac{3.45}{Sin 3^{o} }$

 = $\frac{3.45}{0.05234}$

= 65.9152

l = 65.9 feet

Change in length of ramp = 65.9 - 33.0

                            = 32.9

The ramp should be 32.9 feet longer.