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In this lesson, we will learn how to solve problems involving angles of elevation and depression and use them to find the distance between two objects.

Q1:

The distance between two control towers π΄ and π΅ at an airport is 1β931 meters. The angles of depression from an airplane to π΄ and π΅ are π = 6 1 β and πΌ = 6 5 3 0 β² β respectively and the vertical projection of the plane β π΄ π΅ . Find the vertical altitude of the plane giving the answer to the nearest tenth.

Q2:

Michael wants to find the height of an oak tree in his garden. He decides he needs to make a clinometer in order to measure the angle of elevation. He uses a straw, a protractor, some string, and a bit of Blu-Tack as a weight. Michael stands at a perpendicular distance of 100 ft from the base of the tree and measures the angle on his clinometer to be 5 9 β as seen in the diagram.

Work out the angle of elevation.

Given that Michaelβs eyeline is 6 ft from the ground, work out the height of the tree to the nearest foot.

Q3:

A building is 3 meters tall. The angle of elevation from the top of the building to the top of the tree is , and the angle of depression from the top of the building to the base of the tree is . Find the height of the tree giving the answer to two decimal places.

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