8.5: Angles of Elevation and Depression

  Angle of Elevation    Angle of Depression The angle formed by a horizontal line & an observers line of sight above the horizontal line The angle formed by a horizontal line & an observers line of sight below the horizontal line

Example 1: a) 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 is 27°? tan 27 = 30.5 𝑥 𝑥=58.9 30.5 ft

Example 2: Example 2: 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? tan 52 = 40 𝑥 𝑥=31.25 𝑓𝑡

You Try! 1. A 20-foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. What is the ladder’s angle of elevation? cos Θ = 8 20 cos −1 8 20 =Θ Θ=66.42° 20 ft Θ 8 ft

You Try! 2. A 50-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What is the angle of depression from the top of the tower to the point on the ground where the cable is tied? tan Θ = 50 30 cos −1 50 30 =Θ Θ=59.04° Θ 50 m Θ 30 m

You Try! 3. A person at one end of a 230-foot bridge spots the river’s edge directly below the opposite end of the bridge and finds the angle of depression to be 57. How far below the bridge is the river? 230 ft tan 57 = 𝑥 230 𝑥=354.17 𝑓𝑡 57° x