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Two points on opposite sides of a tower at 30 and 45 degrees: distance between them or the height

This type of question, asked 4 times: 18 Sep 2025 S1, 18 Sep 2025 S3, 24 Sep 2025 S3, 26 Sep 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    18 Sep 2025 S1

    60
    A man standing on the top of a 120 m high tower observes the angles of depression of two cars on opposite sides of the tower to be 30∘30^\circ and 45∘45^\circ. What is the distance between the two cars?

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  2. Question 2

    18 Sep 2025 S3

    60
    An airplane flying at a height of 300 m notices the angles of depression to two boats located on opposite sides as 45∘45^\circ and 30∘30^\circ. Find the distance between the two boats.

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  3. Question 3

    24 Sep 2025 S3

    54
    Two ships positioned on opposite sides of a lighthouse observe the angles of elevation to the top of the lighthouse, which are 30∘30^\circ and 45∘45^\circ respectively. Given that the height of the lighthouse is 100 meters, determine the distance between the two ships.

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  4. Question 4

    26 Sep 2025 S2

    54
    The angles of elevation of the top of a cliff from two points on the ground, 200 m apart, and on opposite sides of the cliff, are 30∘30^\circand 45∘45^\circ. What is the height of the cliff?

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