Warm Up
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
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ANGLES OF DEPRESSION AND ELEVATION, Lecture notes of Mathematics
ANGLES OF DEPRESSION AND ELEVATION MODULE IN TRIGONOMETRY
What you will learn
- How do you identify the pairs of alternate interior angles in a diagram?
- How do you find the height of an object given the angle of elevation and the length of the shadow?
- How do you find the distance between two points using the angle of depression?
Typology: Lecture notes
2020/2021
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Download ANGLES OF DEPRESSION AND ELEVATION and more Lecture notes Mathematics in PDF only on Docsity!
Warm Up
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
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 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 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.
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.
Check It Out! Example 7 What if…? 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. By the Alternate Interior Angles Theorem, m F = 3°. Write a tangent ratio. Multiply both sides by x and divide by tan 3°. x 1717 ft Simplify the expression. 3 °
Example 8: Shipping Application An observer in a lighthouse is 69 ft above the water. He sights two boats in the water directly in front of him. The angle of depression to the nearest boat is 48º. The angle of depression to the other boat is 22º. What is the distance between the two boats? Round to the nearest foot.
Example 8 Continued Step 2 Find y. By the Alternate Interior Angles Theorem, m CAL = 58°. . In ∆ ALC, So
Step 3 Find z. By the Alternate Interior Angles Theorem, m CBL = 22 °. Example 8 Continued In ∆ BLC, So