MPM 2DI Word Problems U7_D5 (measuring inaccessible heights & widths)

Pg 349 #3-8, 9a, 10

Learning Goal: - use SOHCAHTOA to solve real life application problems

Many word problems in this unit involve angles of elevation and angles of depression.

Angle of elevation :- The angle that your line of sight makes with the horizontal. (When looking up).

Angle of depression :- The angle that your line of sight makes with the horizontal. (When looking

down).

*** Notice how both are measured from a horizontal line up or down. ***

CLINOMETER: a slope angle and height meter device Used by:

MPM 2DI Word Problems U7_D5 (measuring inaccessible heights & widths)

Pg 349 #3-8, 9a, 10

Discussion: George uses a clinometer to measure the angle of

elevation of this totem pole. He finds that it is 34. He is standing 4 m away from the base of the pole when he measures the angle. He concludes that the totem pole is 2.7 m tall. George is wrong, why???? Draw a picture and determine whether each statement is true or false. If true, give a

convincing argument.

As you move farther away from a flagpole, the angle of elevation increases.

If you look out the window of a tall building at a car, the angle of depression decreases as the car moves away from you.

If you look at a fountain from the windows of a tall building, the angle of depression decreases as you move to higher and higher floors of the building.

As a bird flies toward you, its angle of elevation increases.

MPM 2DI Word Problems U7_D5 (measuring inaccessible heights & widths)

Pg 349 #3-8, 9a, 10

Draw a picture of each, and then solve.

1. Find to the nearest foot the height of a vertical post if its shadow is 18 feet long when the angle of elevation of the sun is 38o.

2. A ramp is 120 feet long and rises vertically 15 feet. Find the angle of elevation of the ramp.

3. The Chrysler Building in New York is 1046 feet tall. A person stands half a mile away and views the top of the building. Find the angle of elevation. (1 mile = 5280 ft)

4. From an airplane that is flying at an altitude of 300 ft, the angle of depression to a ground signal is 27°. Find the direct-line distance between the airplane and the ground signal.

5. A rescue plane flying above a body of water spots a shipwrecked person at an angle of depression of 40°. If the direct distance between the plane and the person is 105m, how high is the plane flying?

6. A person 2m tall sees a cat in a free at an

angle of elevation of 38 (from his sightline). If the cat is 5m up the tree, how far away from the free is the person standing?