Question

The horizontal distance between two tree of different height is 30m.The angle of depression of the top of the first tree seen from top of the second tree is 30°.find the height of the first tree.​

Answer 1

Answer:

Let the height of the first tree = AB = h.

Let the height of the second tree = CE = 40 m.

The distance between the trees = BC = 30 m.

In ΔADE,

⇒ Tan 30 = DE/AD

⇒ (1/√3) = (40 - h)/30

⇒ 30 = √3(40 - h)

⇒ 30 = 40√3 - √3h

⇒ 30 = 69.28 - 1.732h

⇒ 39.28 = 1.732h

⇒ ~h = 22.68 m.

Therefore, the height of the tree = 22.68 m.

Step-by-step explanation: