8-4: Angles of Elevation 8-4: Angles of Elevation and Depressionand Depression

Expectations:Expectations:1)1) G1.3.1: Define and use sine, cosine and G1.3.1: Define and use sine, cosine and

tangent ratios to solve problems using tangent ratios to solve problems using trigonometric ratios in right triangles.trigonometric ratios in right triangles.

2)2) Determine the exact values of sine, cosine Determine the exact values of sine, cosine and tangent for various angle measures.and tangent for various angle measures.

Daily Quiz 5/16:The hypotenuse of the right triangle ABC shown below is 17 feet long. The cosine of angle C is 3/5. How many feet long is the segment AC?

A. 6

B. 10.2

C. 12

D. 15

E. 28.3 A C

17

B

Angles of ElevationAngles of Elevation

If a situation can be represented If a situation can be represented by a person looking up, we have by a person looking up, we have an angle of elevation.an angle of elevation.

Angles of elevation are always Angles of elevation are always measured off of the horizontal – measured off of the horizontal – never the vertical!!!never the vertical!!!

Angle of ElevationAngle of Elevation

Angles of DepressionAngles of Depression

Angles of depression represent Angles of depression represent situations in which a person situations in which a person looks down.looks down.

Angles of depression are always Angles of depression are always measured off of the horizontal – measured off of the horizontal – never off of the vertical!!!never off of the vertical!!!

Angle of DepressionAngle of Depression

Charo is 50 feet from a totem pole and looks up at an angle of 75° to see the top of the pole. If Charo is 5 feet tall, how tall is the totem pole?

When measured from a point on the ground that is a certain distance from the base of a cell phone tower, the angle of elevation to the top of the tower is 41°. The height of the cell phone tower is 200 feet. What is the distance, in feet, to the cell phone tower?

41°

200 feet (tower)

Distance (?)

A. 200 tan 41B. 200 sin 41C. 200 cos 41D. 200 sec 41E. 200 cot 41

Betty is at the top of a sledding hill. If she looks down at 32° to see the bottom of the hill and the elevation of the hill is known to be 100 feet, how long is the sled run?

A pilot is flying at an altitude of 2,500 feet. If she can see the beginning of the landing strip by looking down at an angle of 6°, what is the ground distance from the airport?

Daily Quiz 5/17

1. Determine the value of x.

2. Determine the value of θ.

12.5

34°

x

10

θ7

Mad Dog McCoy looks up at an angle of 54 degrees to see the top of a flagpole. If she is 30 feet away from the flagpole and she is 5 feet tall, how tall is the flagpole?

Betty is standing on the top of a zip line looking down at Claire at an angle of 18 degrees. If the elevation of the top of the zip line is 65 feet higher than at the bottom, how long is the cable for the zip line?

AssignmentAssignment

pages 423 – 425, pages 423 – 425,

# 17 – 27 (odds), 30, 31, 33 a & b, # 17 – 27 (odds), 30, 31, 33 a & b, 35 – 43 (odds)35 – 43 (odds)