Download presentation

Presentation is loading. Please wait.

1
**Angles of Elevation and Depression**

Geometry Angles of Elevation and Depression CONFIDENTIAL

2
Warm up Find each length: X Y z CONFIDENTIAL

3
**Angles of Elevation and Depression**

An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. In the diagram./1 is the angle of elevation from the tower T to the plane P. Next page CONFIDENTIAL

4
An angle of depression is the angle formed by a horizontal line and a line of a sight to a point below the line./2 is the angle of depression from the plane to the tower. CONFIDENTIAL

5
Since horizontal lines are parallel, /1 ≅ /2 by the Alternate Interior Angles Theorem. Therefore the angle of elevation from one point is congruent to the angle of depression from the other point. CONFIDENTIAL

6
**Classifying Angle of Elevation and Depression**

Classify each angle as an angle of elevation or angle of depression. A ) /3 /3 is formed by a horizontal line and a line of sight to a point below the line. It is an angle of depression. B) /4 /4 is formed by a horizontal line and a line of sight to a point above the line. It is an angle of elevation. CONFIDENTIAL

7
Now you try! 1) Use the diagram to classify each angle as an angle of elevation or angle of depression. 1a. / b. /6 CONFIDENTIAL

8
**Finding Distance by Using Angle of Elevation**

An air traffic controller at an airport sights a plane at an angle of elevation of 41˚. The pilot reports that plane’s altitude is 4000 ft. What is the horizontal distance between the plane and the airport? Round to the nearest foot. Let x be the horizontal distance between the plane and the airport. Let A represent the airport and P represent the plane P 4000 ft 41˚ A Next page x CONFIDENTIAL

9
**Multiply both sides by x and divide both sides by tan41˚.**

4000 ft 41˚ A x You are given the side opposite /A, and x is the side adjacent to /A. So write a tangent ratio. Multiply both sides by x and divide both sides by tan41˚. Simplify the expression. CONFIDENTIAL

10
Now you try! 2) What if….? Suppose the plane is at an altitude of 3500ft and the angle of elevation from the airport to the plane is 29˚. What is the horizontal distance between the plane and the airport? Round to the nearest foot. CONFIDENTIAL

11
**Finding Distance by Using Angle of Depression**

A forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is 7˚. What is the horizontal distance between the tower and the fire? Round to the nearest foot. Let T represent the top of the tower and let F represent the fire. Let x be the horizontal distance between the tower and the fire. 90 ft T F 7˚ S x Next page CONFIDENTIAL

12
**By the Alternate Interior Theorem, m/F = 7˚.**

90 ft T S x 7˚ By the Alternate Interior Theorem, m/F = 7˚. write a tangent ratio. Multiply both sides by x and divide both sides by tan7˚. Simplify the expression. CONFIDENTIAL

13
Now you try! 3) Suppose the ranger sees another fire and the angle of depression to the fire is 3˚. What is the horizontal distance to this fire? Round to the nearest foot. 90 ft T S x 3˚ CONFIDENTIAL

14
Aviation Application A pilot flying at an altitude of 2.7 km sights two control towers directly in front of her. The angle of depression to the base of one tower is 37˚. The angle of depression to the base of the other tower is 58 ˚. What is the distance between the two towers? Round to the nearest tenth of a kilometer. Step: 1 Let P represent the plane and let A and B represent the two towers. Let x be the distance between the towers. Next page CONFIDENTIAL

15
**By the Alternate Interior Angle Theorem, m/ CAP = 58˚**

Step 2 Find y. By the Alternate Interior Angle Theorem, m/ CAP = 58˚ Next page CONFIDENTIAL

16
**By the Alternate Interior Angle Theorem, m/ CBP = 37˚**

Step 3 Find Z. By the Alternate Interior Angle Theorem, m/ CBP = 37˚ Next page CONFIDENTIAL

17
**So the two towers are about 1.9 km. apart.**

Step 4 Find x. x = z – y x = – = 1.9 km. So the two towers are about 1.9 km. apart. CONFIDENTIAL

18
Now you try! 4) A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78˚, and the angle of depression to the second airport is 19˚. What is the distance between the airport? Round to the nearest foot. CONFIDENTIAL

19
**Now some practice problems for you!**

CONFIDENTIAL

20
**Classify each angle as an angle of elevation or angle of depression.**

Assessment Classify each angle as an angle of elevation or angle of depression. 1 ) /1 /2 /3 4) /4 CONFIDENTIAL

21
5) When the angle of elevation to the sun is 37˚, a flagpole casts a shadow that is 24.2 ft long. What is the height of the flagpole to the nearest foot? CONFIDENTIAL

22
6) The pilot of a traffic helicopter sights an accident at an angle of depression of 18˚. The helicopter’s altitude is 1560 ft. What is the horizontal distance from the helicopter to the accident? Round to the nearest foot. CONFIDENTIAL

23
7) From the top of a canyon, the angle of depression to the far side of the river is 58˚, and the angle of depression to the near side of the river is 74˚.The depth of the canyon is 191 m. What is the width of the river at the bottom of the canyon? Round to the nearest tenth of a meter. CONFIDENTIAL

24
**Angles of Elevation and Depression**

Let’s review Angles of Elevation and Depression An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. In the diagram./1 is the angle of elevation from the tower T to the plane P. An angle of depression is the angle formed by a horizontal line and a line of a sight to a point below the line./2 is the angle of depression from the plane to the tower. CONFIDENTIAL

25
Since horizontal lines are parallel, /1 ≅ /2 by the Alternate Interior Angles Theorem. Therefore the angle of elevation from one point is congruent to the angle of depression from the other point. CONFIDENTIAL

26
**Classifying Angle of Elevation and Depression**

Classify each angle as an angle of elevation or angle of depression. A /3 /3 is formed by a horizontal line and a line of sight to a point below the line. It is an angle of depression. B /4 /4 is formed by a horizontal line and a line of sight to a point above the line. It is an angle of elevation. CONFIDENTIAL

27
**Finding Distance by Using Angle of Elevation**

An air traffic controller at an airport sights a plane at an angle of elevation of 41˚. The pilot reports that plane’s altitude is 4000 ft. What is the horizontal distance between the plane and the airport? Round to the nearest foot. Let x be the horizontal distance between the plane and the airport. Let A represent the airport and P represent the plane P 4000 ft 41˚ A Next page x CONFIDENTIAL

28
**Multiply both sides by x and divide both sides by tan41˚.**

4000 ft 41˚ A x You are given the side opposite /A, and x is the side adjacent to /A. So write a tangent ratio. Multiply both sides by x and divide both sides by tan41˚. Simplify the expression. CONFIDENTIAL

29
**Finding Distance by Using Angle of Depression**

A forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is 7˚. What is the horizontal distance between the tower and the fire? Round to the nearest foot. Let T represent the top of the tower and let F represent the fire. Let x be the horizontal distance between the tower and the fire. 7˚ 90 ft x Next page CONFIDENTIAL

30
**By the Alternate Interior Theorem, m/F = 7˚.**

90 ft S x By the Alternate Interior Theorem, m/F = 7˚. write a tangent ratio. Multiply both sides by x and divide both sides by tan7˚. Simplify the expression. CONFIDENTIAL

31
**You did a great job today!**

CONFIDENTIAL

Similar presentations

Presentation is loading. Please wait....

OK

Applications of Right Triangles

Applications of Right Triangles

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google