Question

1. Joshua has a ladder that is 15 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height (2 points)? Show your work and draw a diagram to support your answer

Answer 1

Unsafe; angle with ground > 70°.

Explanation:

Data:

a = 15 ft

b = 14.8 ft

A = 90°

Calculation:

We can use the Law of Sines.

`\begin{array}{rcl}(a)/(\sin A ) & = & (b)/(\sin B )\\\\(15)/(\sin 90^(\circ)) & = & (14.8)/(\sin B)\\\\(15)/(1) & = & (14.8)/(\sin B)\\\\15\sin B & = & 14.8\\\sin B & = & 0.9867\\B & = &\arcsin 0.9867\\& = & \boxed{\mathbf{80.63^(\circ)}}\\\end{array}`

The ladder will be unsafe because its angle with the ground is greater than 70°.