Question

A handicap access ramp is being constructed. To meet requirements, the ramp must be built so that the angle of elevation is θ. The ramp must rise a total of h feet (this is the distance the door is from the ground). Find the length of the ramp to the nearest tenth of a foot.

a) h×tan(θ)
b) h/sin(θ)
c) h/cos(θ)
d) h/tan(θ)

Answer 1

The length of a handicap access ramp given the rise (h) and the angle of elevation (θ) can be solved using trigonometry, where the formula for the ramp length is h/sin(θ) to meet accessibility requirements.

Step-by-step explanation:

To determine the length of the handicap access ramp to the nearest tenth of a foot, one must consider the rise of the ramp (h) and the angle of elevation (θ). Given that the ramp must meet requirements, the appropriate trigonometric function relating the angle of elevation, the height (rise), and the length of the ramp (hypotenuse) must be used.

In a right-angled triangle, the length of the ramp will be the hypotenuse. Considering the definitions of trigonometric functions, the correct length of the ramp is calculated by the formula:

θ = sin-1 (h / hypotenuse)

Therefore, rearranged to find the hypotenuse (the length of the ramp), the formula becomes:

Ramp length = h / sin(θ)

So, the correct calculation for finding the length of the ramp is option b) h/sin(θ).