15 - 3D Trig Problems - Notes PDF

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15 - 3D Trig Problems

MPM2D – Trigonometry

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3D Tr Triigon ono ome metr tr try y Pr Prob ob obllem emss Some problems in trigonometry involve more than one triangle. A sketch is crucial when trying to solve these types of problems. Example 1 To calculate the height of an inaccessible cliff, data is collected and recorded on the diagram below. Calculate the height of the cliff to the nearest centimetre.

Example 2 The angle of elevation to the top of the tree is 72°. How tall is the tree? Triangle ABC is on a horizontal plane.

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15 - 3D Trig Problems

MPM2D – Trigonometry

Example 3 Two roads intersect at 34°. At 9:00 am, two cars leave the intersection in different directions at speeds of 80 km/h and 100 km/h. 15 minutes later, a traffic helicopter is right above the slower car, at a height of 1500 m. Determine the angle of depression to the faster car and distance from the helicopter to the faster car (along the ground).

Example 4 From the top of a 50 m high bridge, two boats are seen at anchor. One boat is 50° west of due south and has an angle of depression of 38°. The other boat is 60° east of due south and has a 35° angle of depression. How far apart are the boats?

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15 - 3D Trig Problems

MPM2D – Trigonometry

Example 5 A ship is sailing due east at night. The ship's navigator spots a lighthouse in the direction of 40° east of north. According to the map, the water within 400 m of the lighthouse is too shallow for the ship. After the ship continues to sail east for 800 m, the new direction of the lighthouse from the ship is 48° west of north.

a) How far away is the lighthouse now?

b) How close did the boat come to the lighthouse?

c) Was the ship ever within the 400 m range of shallow water?

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15 - 3D Trig Problems

MPM2D – Trigonometry

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