Question

A river is 60 m wide. A tree of unknown height is on one bank. The angle
of elevation of the top of the tree from the point exactly opposite to the
foot of the tree, on the other bank, is 30°. Find the height of the tree.​

Answer 1

Answer:

the height of the tree is 1800 m

Step-by-step explanation:

30 = x / 60

x = 60 × 30

x = 1800 m

Answer 2

Consider AB as the tree and BC as the width of the river

C is the point which is exactly opposite to B on the other bank and 30⁰ is the angle of elevation

Take height of the tree AB = x m

Width of the river BC = 60 m

We know that

tan θ = AB/CB

Substituting the values

tan 30⁰ = x/60

So we get

1/√3 = x/60

By cross multiplication

x = 60/√3

Multiplying and dividing by √3

x = 60/√3 × √3/√3

x = 60√3/3 = 20√3

Substituting the value of √3

x = 20 (1.732)

x = 34.640

x = 34.64 m

Hence, the height of the tree is 34.64 m.