Q. 41 A3.7( 3 Votes )

# From an aeroplane, the angles of depression of two ships in a river on left and right of it are 60° and 45° respectively. If the distance between the two ships is 100m, find the height of the aeroplane.

Answer :

In right Δ ABP, we have

…(i)

In the right Δ ABQ, we have

⇒ 100 – x = h

⇒ 100 = h + x

[from (i)]

Multiplying and divide by the conjugate of √3 + 1, we get

[∵ (a – b)(a + b) = (a^{2} – b^{2})]

⇒ h = 50 (3 - √3)

⇒ h = 50 (3 – 1.732) [∵ √3 = 1.732]

⇒ h = 50 (1.268)

⇒ h = 63.4 m

Hence, the height of the aeroplane is 63.4m

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PREVIOUSAt a point P on the ground, the angles of elevation of the top of a 10 m tall building, and of a helicopter covering some distance over the top of the building, are 30° and 60° respectively. Find the height of the helicopter above the ground.NEXTThere is a small island in the middle of 100 m wide river. There is a tall tree on the island. Points P and Q are points directly opposite each other on the two banks and in line with the tree. If the angles of elevation of the top of the tree at P and Q are 30° and 45°, find the height of the tree.

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