Question

1.There is a small island in the middle of a 100 m wide river and a tall tree

stands on the island. P and Q are the points directly opposite to each other

on the two banks, and in a line with the tree. If the angles of elevation of

the top of tree from P and Q are 30° and 45° respectively, find the height

of the tree.​

Answer 1

Answer:

The height of the tree is 36.33 m.

Step-by-step explanation:

Let PQ be the width of the river and RS be the height of the tree on the island.

In rt.△PRS,

x = RS cot 30°

x = RS √3

x = √3 RS ........(i)

In rt.△RSQ,

SQ = RS cot 45°

(100-x) = RS

x=100 - RS ........(ii)

Equating (i) and (ii) we have:

√3 RS = 100 - RS

2.73 RS = 100

RS = 36.63 m

Therefore the height of the tree is 36.33 m.

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Hope it helped (◕ᴗ◕✿)(◔‿◔)