Question

A 12-foot high ladder reaches a tree limb when it leans at a 36 degree angle with the ground. Approximately how far away is the base of the ladder from the tree trunk base?

Answer 1

Look at the picture.

$\cos 36^\circ = \frac{x}{12} \\ 0.809 \approx \frac{x}{12} \\ 0.809 \times 12 \approx x \\ x \approx 9.708$

The base of the ladder is approximately 9.708 feet from the tree trunk base.