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Applying Angles of Elevation and Depression to Solve Word Problems

In this lesson, students will explore the concepts of angles of elevation and depression through practical word problems. They will learn to apply trigonometric principles to determine distances and heights in real-world scenarios, such as calculating the distance to a sailboat from a lighthouse or finding the height of a cliff from a given angle of elevation. The session includes checks on homework and a trigonometry review, with various examples to reinforce understanding. Visual aids, including diagrams and problems involving ladders and kites, will help engage students.

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Applying Angles of Elevation and Depression to Solve Word Problems

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  1. Warm Up 3/10/13 • Solve for the variables • Simplify x y y

  2. Agenda • Warm Up • Homework Check • Review Trigonometry • Angles of Elevation and Depression

  3. Homework Check 1) 2) 3) 4) 5) 6) 7) 8) 9)

  4. Homework Check • 2. 2. 3. 4. 5. 6. 5. 6) 9) 15)

  5. Trigonometry Review To Solve for Sides To Solve for Angles

  6. Today’s Objective Students will apply Angles of Depression and Elevation to solve word problems.

  7. Angle of Depression The Angle of Depression is the angle from the “sky to the line”

  8. Angle of Elevation The Angle of Elevation is the angle from the “ground to the line”

  9. Suppose an operator at the top of a lighthouse sights a sailboat at a 2oangle of depression. If the top of the lighthouse is 25m above sea level, what is the distance x between the boat and the operator in the lighthouse to the nearest integer? x 25

  10. Claim: angle of depression = angle of elevation • Why?

  11. ALWAYS DRAW A PICTURE!!! The angle of elevation from point A to the top of a cliff is 38*. If point A is 80 feet from the base of the cliff, how high is the cliff?

  12. 2. From the top of a tower, the angle of depression to a stake on the ground is 72*. The top of the tower is 80 feet above ground. How far is the stake from the foot of the tower?

  13. 3. A tree 40 feet high casts a shadow 58 feet long. Find the measure of the angle of elevation of the sun.

  14. 4. A ladder leaning against a house makes an angle of 60* with the ground. The foot of the ladder is 7 feet from the foundation of the house. How long is the ladder?

  15. 5. A kite on a 40-foot string makes a 50* angle with the ground. How high above the ground is the kite?

  16. Classwork/Homework • Angles of Depression/Elevation Worksheet

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