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Revisions

Scale Diagrams

Grade

10

Term

3

  1. From the perspective of an observer, define the "angle of elevation".

  2. From the perspective of an observer, define the "angle of depression".

  3. An observer on top of a 60m tall lighthouse sees a boat at sea. The horizontal line from the observer's eye is parallel to the sea level. Is the angle between the horizontal line and the line of sight to the boat an angle of elevation or depression?

  4. If a scale of 1 cm : 10 m is used for a diagram, what length on the diagram would represent an actual distance of 60 m?

  5. A tree casts a shadow 6 m long. The angle of elevation from the tip of the shadow to the top of the tree is 50∘. Draw a rough sketch to represent this situation.

  6. Using a scale of 1 cm represents 1 m, create a scale diagram for the situation in question 5 and find the height of the tree.

  7. From a 60 m tall lighthouse, a boat A is observed with an angle of depression of 31∘, and another boat B is observed with an angle of depression of 45∘. The boats and the lighthouse are in the same vertical plane. Find the distance between the boats using a scale diagram.

  8. An observer stands 5 m away from a netball goalpost. The angle of elevation to the top of the post is 18∘ from eye level, and the angle of depression to the base of the post is 15∘. Using a scale diagram, find the height of the observer.

  9. Using the information and scale diagram from question 8, find the height of the goalpost.

  10. What instrument is used to measure angles of elevation and depression?

  11. From a point A on the ground, the angle of elevation to the top of a mango tree is 30∘. From point B, which is 10 m closer to the tree, the angle of elevation is 40∘. Use a scale diagram to find the height of the tree.

  12. An observer on a horizontal ground 3 m away from a bell tower observes the top of the tower with an angle of elevation of 60∘ and the bottom with an angle of depression of 25∘. Find the height of the tower using a scale diagram.

  13. A ramp for wheelchair access is 10 m long and rises to a height of 1 m. Draw a scale diagram and find the angle the ramp makes with the horizontal ground.

  14. From the top of a building, the angle of depression to a car on the ground is 40∘. From a window 10 m directly below the top, the angle of depression to the same car is 30∘. Find the height of the building.

  15. From a point A on the ground, the angle of elevation to the top of a cliff is 35∘. After walking 100 m towards the cliff to a point B, the angle of elevation is 50∘. Find the distance from point B to the base of the cliff.

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