Question

plz tell me answer with diagram​

Answer 1

QUESTION:-

A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60˚. When he moves 40 m, away from the bank, he finds the angle of elevation to be 30˚.Find the height of tree.

✿SOLUTION✿

★let

★The height of tree be h

•In right angle triangle BAE

$⇒tan60 = \frac{ba}{be} \\ \\ ⇒ \sqrt{3} = \frac{h}{be} \\ \\ ⇒h = be \sqrt{3} ......(1)$

•In right angle triangle BAC

$⇒tan30 = \frac{ba}{ac} \\ \\ ⇒ \frac{1}{ \sqrt{3} } = \frac{h}{be + 40} \\ \\ ⇒h \sqrt{3 } = be + 40 \\ \\ ⇒h = \frac{be + 40}{ \sqrt{3} }.....(2)$

now putting together 1 and 2

$⇒be \sqrt{3} = \frac{be + 40}{ \sqrt{3} } \\ \\ ⇒be \sqrt{9} = be + 40 \\ \\ ⇒3be = be + 40 \\ \\ ⇒2be = 40 \\ \\ ⇒be = 20$

Hence:-

the height of tree=be√3

=20√3m