Question

The two palm trees are of equal heights and are standing opposite each other on either side of the river, which is 80 m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees and the distances of the point O from the trees.​

Answer 1

Given measures according to the question

ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴛʀᴇᴇs = 34.64 m

ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴛʀᴇᴇs = 34.64 m

ᴅɪsᴛᴀɴᴄᴇ = 60 m.

Let Palm tree be poles

tan600=80-xb

3=80-xb

b=3x-803 ....(i)

and,

tan300=31=xa

x=a3 ...(ii)

b=3a-803

Or

3a-b=803

❥︎ Now it is given that the heights are equal.

Hence

a=b=h

Therefore

2h=803

h=203

=2(17.32)

=34.64m

Hence

x= h3

=20(3)=60m

Answer 2

Let Palm tree be poles

tan600=80-xb

3=80-xb

b=3x-803 ....(i)

and,

tan300=31=xa

x=a3 ...(ii)

b=3a-803

Or

3a-b=803

❥︎ Now it is given that the heights are equal.

Hence

a=b=h

Therefore

2h=803

h=203

=2(17.32)

=34.64m

Hence

x= h3

=20(3)=60m