Question

Joshua has a ladder that is 19 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 15 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.

Answer 1

50.47°

Explanation:

We can use the trigonometric function sine to determine the angle the ladder makes with the ground. Let's call this angle theta. We have:

sin(theta) = opposite/hypotenuse

where the opposite side is the height of the ladder on the wall (15 ft) and the hypotenuse is the length of the ladder (19 ft). Solving for theta, we get:

theta = sin^-1(15/19) ≈ 50.47°

Since this angle is less than 75°, the ladder will be safe at this height.