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Trigonometry

Trigonometry. Angles of elevation and depression. Instructions for use. There are 5 worked examples shown in this PowerPoint plus explanations. A red dot will appear top right of screen to proceed to the next slide.

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Trigonometry

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  1. Trigonometry Angles of elevation and depression

  2. Instructions for use • There are 5 worked examples shown in this PowerPoint plus explanations. • A red dot will appear top right of screen to proceed to the next slide. • Click on either the navigation buttons or use the cursor keys to access the relevant slides.

  3. Angle of elevation The angle of elevation is the angle formed by the line of sight and the horizontal line of sight x horizontal

  4. horizontal horizontal Angle of depression x The angle of depression is the angle formed by the line of sight and the horizontal line of sight

  5. horizontal horizontal Combining the two x depression line of sight elevation x It’s alternate angles all over again!

  6. B h m 250 A 21 Example 1 The angle of elevation of building A to building B is 250. The distance between the buildings is 21 metres. Calculate how much taller Building B is than building A. Angle of elevation Step 1: Draw a right angled triangle with the given information. Step 2: Take care with placement of the angle of elevation Step 3: Set up the trig equation. Step 4: Solve the trig equation.

  7. 80 m  60 m Example 2 A boat is 60 metres out to sea. Madge is standing on a cliff 80 metres high. What is the angle of depression from the top of the cliff to the boat? Step 1: Draw a right angled triangle with the given information. Angle of depression Step 2: Use your knowledge of alternate angles to place inside the triangle. Step 3: Decide which trig ratio to use. Step 4: Use calculator to find the value of the unknown.

  8. Plane 25 km h Example 3 Marty is standing on level ground when he sees a plane directly overhead. The angle of elevation of the plane after it has travelled 25 km is 200. Calculate the altitude of the plane at this time. Step 1: Draw a right angled triangle with the given information. 200 Step 2: Use your knowledge of alternate angles to place 200 inside the triangle. Angle of elevation 200 Step 3: Decide which trig ratio to use. Step 4: Use calculator to find the value of the unknown. (nearest km)

  9. 5m 650 450 P K p k Example 4 Kate and Petra are on opposite sides of a tree. The angle of elevation to the top of the tree from Kate is 45o and from Petra is 65o. If the tree is 5 m tall, who is closer to the tree, Kate or Petra? Step 1: Draw a diagram Step 2: Set up the trig equations in two parts. Step 3: Solve the equations and answer the question. Kate Petra Answer Therefore, Petra is closer to the tree, since the distance is shorter.

  10. Bird 400 200 2 m Car Example 5 Maryann is peering outside her window. From her window she sees her car and a bird hovering above her car. The angle of depression of Maryann’s car is 200 whilst the angle of elevation to the bird is 400. If Maryann’s window is 2m off the ground, what is the bird’s altitude at that moment? Step 1: Draw a diagram Step 2: Set up the trig equations in two parts. Find d first, then b. Step 3: Solve the equations and answer the question. b d Therefore, The bird is 10.1m (5.5 + 4.6) from the ground at that moment.

  11. Last slide Use the navigation buttons to repeat selected slides

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