Section 7-5 Angle of Elevation – an angle formed by a horizontal line and the line of sight to an object above the line Angle of Depression – an angle formed by a horizontal line and the line of sight to an object below the line angle of depression

angle of elevation

EX: 1. Sam is flying a kite and has let out all of the 35ft. of string that is attached to the kite. If the kite string leaves Sam's hand at an angle of elevation of 48, how high is the kite actually flying?

(ans.) First draw a diagram Second, solve for x. sin 48 = 35x x = 35(sin (48)) x = 26.01 ft.

kite

kite string 35 ft.

x

48 Sam

2. A plane begins its descent as it prepares to land. If it is flying at an altitude of 35,000 ft, and is a ground distance of 48 miles (or 253,440 ft) from the landing strip, at what angle of depression should the plane descend to make a perfect landing? (ans.) Draw a diagram. Set up and Solution: 35000 tan x  253440

plane x 35,000 ft. x 253,440 ft *the red x comes as a result of the alternate interior angle theorem

runway

35000 x = tan-1 ( 253440 ) x = 7.86

3. Katie is standing at the base of a HUGE mountain. She knows that the altitude at the top of the mountain is 6,278 ft. She uses her angleometer (fictitious angle finding device) to find that the mountain rises roughly at an angle of 39 from the base to the top. What is the actual distance she will climb as she travels up the side of the mountain? (ans.) Diagram: Top of mountain

6278 ft.

x

39 Katie

Set up and Solution: sin 39 = 6278 x x(sin (39)) = 6278 6278 x = sin(39) x = 9975.8 ft. or 1.89mi.