A rescue team 1000 ft away from the base of a vertical cliff measures the angle of elevation to the top of the cliff to be 70 degrees A climber is stranded on a ledge. The angle of elevation to the ledge is 55 degrees. How far is the stronded climber from the top of the cliff? Round your answer to the nearest tenth.

To find out how far the stranded climber is from the top of the cliff, we can break the problem into two parts, calculating the height of the cliff and the height of the ledge using trigonometric functions. 1. The height of the cliff (h) can be found using: \( h = 1000 \cdot \tan(70^\circ) \) This gives us approximately \( h \approx 1000 \cdot 2.747 \approx 2747 \) ft. 2. The height of the ledge (l) is: \( l = 1000 \cdot \tan(55^\circ) \) This results in approximately \( l \approx 1000 \cdot 1.428 \approx 1428 \) ft. Now we subtract the height of the ledge from the height of the cliff: Distance from the top of the cliff to the climber = \( 2747 - 1428 \approx 1319 \) ft. So, the stranded climber is approximately **1319.0 ft** away from the top of the cliff.