Applications & Models 4.8

A B C a b c A + B = 90° since C = 90° and A + B + C = 180°

Example 1: Solving a Right Triangle Solve the right triangle shown for all unknown sides and angles. c A B a b=19.4 C 34.2°

Elevation versus Depression Refer back to 4.3 notes for angles of elevation and angles of depression. The tree and submarine pictures, remember?

Example 2: Finding a Side of a Right Triangle A)A safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. A fire department’s longest ladder is 110 feet. What is the maximum safe rescue height?

Example 2: continued B)At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 35°, angle of elevation to the top is 53°. Find the height of the smokestack alone.

Example 3: Finding an Angle of Depression A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool.