Find x and y. Problem of the Day 4

Section 8-5 Angles of Elevation and Depression

Then Now Objectives You used similar triangles to measure distances indirectly. Solve problems involving angles of elevation and depression.

Common Core State Standards Content Standards G.SRT.8 – Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Mathematical Practices 1) Make sense of problems and persevere in solving them. 4) Model with mathematics. Common Core State Standards

An angle of elevation is the angle formed by a horizontal line and an observer’s line of sight to an object above the horizontal line. An angle of depression is the angle formed by a horizontal line and an observer’s line of sight to an object below the horizontal line. Vocabulary

The cross bar of a goalpost is 10 feet high The cross bar of a goalpost is 10 feet high. If a field goal attempt is made 25 yards from the base of the goalpost that clears the goal by 1 foot, what is the smallest angle of elevation at which the ball could have been kicked to the nearest degree? Example 1

At the circus, a person in the audience at ground level watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat’s head is 27°? Example 1

A lifeguard is watching a beach from a line of sight 6 feet above the ground. She sees a swimmer at an angle of depression of 8°. How far away from the tower is the swimmer? Example 2

Maria is at the top of a cliff and sees a seal in the water Maria is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of depression is 52°, what is the horizontal distance from the seal to the cliff to the nearest foot? Example 2

p.583 #1, 2, 4 – 7, 13, 15, 16 Homework

Kyle is on top of a boat 30 feet above the ocean Kyle is on top of a boat 30 feet above the ocean. His eye level is 3 feet above the boat. He is using binoculars to watch a whale surface. If the angle of depression of the whale is 20°, how far is the whale from Kyle’s binoculars? Problem of the Day