Problem 1: Safety of the Ladder

To determine whether Zachary will be safe on the ladder, we need to calculate the angle between the ladder and the ground. The ladder's length and the height to the window are given, so we can use trigonometry to find the angle.

Given:

• Ladder length ( l = 17 ) ft
• Height of the window ( h = 15 ) ft

The angle (\theta) between the ladder and the ground can be found using the sine function:

[ \sin(\theta) = \frac{h}{l} = \frac{15}{17} ]

Now, calculate (\theta):

[ \theta = \sin^{-1}\left(\frac{15}{17}\right) ]

Using a calculator:

[ \theta \approx \sin^{-1}(0.8824) \approx 62.7^\circ ]

To be safe, the angle of elevation between the ladder and the ground should be between 73° and 78°. Since 62.7° is outside this safe range, Zachary is not safe on the ladder.

Summary

Zachary is not safe on the ladder because the angle of elevation (62.7°) is outside the safe range of 73° to 78°.