Question

A fishing lodge wants to build a new boat ramp. The slope of the ramp must be 8° to the horizontal. The total height of the bank is 2.8 m. How long must the sloping section of the ramp be? Give your answer to the nearest centimetre.

Answer 1

Answer:

The length of the sloping section of the ramp is 20.12 m

Step-by-step explanation:

Given;

the total height of the bank, h = 2.8 m

The slope of the ramp must be 8° to the horizontal, i.e, θ = 8°

Let the length of the sloping section = L

let the horizontal distance between the height of the bank and sloping section = b

Thus, h, L and b forms three sides of a right angled-triangle, with L as the hypotenuse side, h  (height of the triangle) as the opposite side and b  (base of the triangle) as the adjacent side.

We determine L by applying the following formula;

Sinθ = opposite / hypotenuse

Sin θ = h / L

L = h / Sin θ

L = 2.8 / Sin 8

L = 2.8 / 0.13917

L = 20.12 m

Therefore, the length of the sloping section of the ramp is 20.12 m