Question

A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. If specifications call for the ladder's angle of elevation to be between 35 and 45 degrees.

Given the information above, sketch out the scenario. Determine if the placement of this ladder satisfies safety specifications. Then, explain why or why not it would meet the safety specifications using at least 3 complete sentences.

Answer 1

Explanation:

Note that the base of the building forms a right angle with the ground and the ladder forms a right triangle with the building.

On this case, we can apply Pythagorean theorem.

Since the ladder serves as the hypotenuse and the distance from the base of the building to the foot of the ladder is adjacent with the angle of elevation, we can use cosine.

Let A be the angle of elevation

cos A = adjacent/hypotenuse

cos A = 10ft/20ft

cos A = 0.50

A = Arc cos 0.50

A = 60°

With the given data, the angle of elevation turns out to be 60°. As it's beyond the allowable values, it won't satisfy the safety specifications of 35°-45°. The placement of the ladder is too steep and would need to be adjusted.