4th 6th 7th

1.Taylor Woolfolk Free

2 Wheat Gregory Alcantar

3 Harrell King Simpson

4 Crum Shabazz Goodrum

5 Scott Klyce S. Harris

6 Holland R. Harris Walton

7 Lawson Corker Tate

12 Oneil Burns Eiland

13 Jordan Nelson Black

14 Oatis C.Johnson Pierce

11 Burnett Stokes Robinson

16 Spikener G. Brown Anderson

Names for Homework Assignments.

Bell Ringer: 3 minutes after the bell

1. Identify the pairs of alternate interior angles.

2. Use your calculator to find tan 30° to the nearest hundredth.

3. Solve . Round to the nearest

hundredth.

2 and 7; 3 and 6

0.58

1816.36

Geometry HR Date: 4/22/2013

Question: How do we measure the immeasurable?

Obj: SWBAT solve problems involving angles of

elevation and depression.

Bell Ringer: See overhead

HW Requests: Kuta Worksheet,,

Parking Lot: Red WB 103, 104 pg 101, 102

Homework: Read Section 8.5

pg 577 #1-7, 12-16 Assign problems

for putting on board

• Announcements:

• Quiz Friday

Geometry IB 4/22/13

Obj: SWBAT solve problems involving angles of

elevation and depression. Question: How do we measure the immeasurable?

Agenda

• Bell Ringer: See overhead

• Homework Requests: Red WB pg 103, Kuta

Worksheet

• Parking lot: Red WB #104, 101,

Homework:Read Section 8.5

pg 577 #1-7, 12-16 Assign problems

• Announcements:

• Quiz Fri.

11.3 Angles of Elevation and

Depression

Solve problems involving angles of elevation and angles of depression.

Angle of Elevation –angle between the line of sight and the

horizontal when looking upward.

Find horizontal line (eye level) and then angle (raise arm). Make

a drawing.

Line of

sight

Angle of Depression –angle between the horizontal and the line

of sight when an observer looks downward.

Find horizontal line (eye level) and then angle (lower arm). Make

a drawing.

Line of sight

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 sight to a point below the line. 2 is the angle of depression from the plane to the tower.

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.

Example 1: Classifying Angles of Elevation and

Depression

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

1

1 is formed by a horizontal line and a line of sight to a point below the line. It is an angle of depression.

Example 2: Classifying Angles of Elevation and

Depression

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

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.

Check It Out! Example 3

Use the diagram above to classify each angle as an angle of elevation or angle of depression.

3a. 5

3b. 6

6 is formed by a horizontal line and a line of sight to a point above the line. It is an angle of elevation.

5 is formed by a horizontal line and a line of sight to a point below the line. It is an angle of depression.

Example 4: Finding Distance by Using Angle of

Elevation

The Seattle Space Needle casts a 67-meter shadow. If the angle of elevation from the tip of the shadow to the top of the Space Needle is 70º, how tall is the Space Needle? Round to the nearest meter.

Draw a sketch to represent the given information. Let A represent the tip of the shadow, and let B represent the top of the Space Needle. Let y be the height of the Space Needle.

Example 4 Continued

You are given the side adjacent to

A, and y is the side opposite A.

So write a tangent ratio.

y = 67 tan 70° Multiply both sides by 67.

y 184 m Simplify the expression.

Check It Out! Example 5

What if…? Suppose the plane is at an altitude of 3500 ft 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.

3500 ft

29°

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 by tan 29°.

x 6314 ft Simplify the expression.

Example 6: Finding Distance by Using Angle of

Depression

An ice climber stands at the edge of a crevasse that is 115 ft wide. The angle of depression from the edge where she stands to the bottom of the opposite side is 52º. How deep is the crevasse at this point? Round to the nearest foot.

Example 6 Continued

Draw a sketch to represent the given information. Let C represent the ice climber and let B represent the bottom of the opposite side of the crevasse. Let y be the depth of the crevasse.

Example 6 Continued

By the Alternate Interior Angles Theorem, mB = 52°.

Write a tangent ratio.

y = 115 tan 52° Multiply both sides by 115.

y 147 ft Simplify the expression.

Exit Ticket: Angle of Elevation and Depression

Exit Ticket: See below #1

1. Find the angle of elevation of

the sun when a 6-meter flagpole casts

a 17-meter shadow.

2. After flying at an altitude of 575 meters,

a helicopter starts to descend when its

ground distance from the landing pad is 13.5

kilometers. What is the angle of depression

for this part of the flight?

3. The top of a signal tower is 250 feet above sea

level. The angle of depression from the top of

the tower to a passing ship is 19°. How far is

the foot of the tower from the ship?

@ 1. about 19.4° 2. about 2.4° 3. about 726 ft

Line of

sight

Line of sight