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Observer at height h sees two objects on opposite sides at 30 and 45 degrees: distance between them

The same question, asked 3 times: 18 Sep 2025 S1*, 18 Sep 2025 S3*, 24 Sep 2025 S3. Every wording 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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