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From the top of a pole or tower, angle to the top of another structure: find distance or height (height difference = distance x tan)

This type of question, asked 3 times: 3 Mar 2023 Tier II, 6 Mar 2023 Tier II, 26 Oct 2023 Tier II. All 3 questions below, oldest first.

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  1. Question 1

    3 Mar 2023 Tier II

    30
    From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60∘60^\circ. If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower?

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  2. Question 2

    6 Mar 2023 Tier II

    25
    From the top of an upright pole 24324\sqrt{3} feet high, the angle of elevation of the top of an upright tower was 60∘60^\circ. If the foot of the pole was 60 feet away from the foot of the tower, what tall (in feet) was the tower?

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  3. Question 3

    26 Oct 2023 Tier II

    2
    From the top of a tower, the angle of depression of the top of a 10 m high building is 60∘60^\circ. If the distance between the tower and the building is 50350\sqrt{3} m, find the height of the tower.

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