Question

from a point on the ground the top of a tree seem to have an angle of elevation 60 degree the distance between the tree and the point is 50 metre calculate the height of the tree ​

Answer 1

86.6

i think this is the answer

Answer 2

Given,

The angle of elevation from a point on the ground to the top of a tree = 60°,

Distance between the tree and the observation point = 50 m.

To find,

Height of the tree.

Solution,

Firstly, let the height of the tree be 'h' meters.

Now, it can be seen that if we suppose the top of the tree to be A, the foot of the tree be B, and the point of observation to be C, what we get is a right triangle, that is ΔABC right angled at B.

In ΔABC,

AB = h (assumed above),

∠ABC = 90° (∵ ΔABC is right angled at B),

∠ACB = 60° (given), and

BC = 50 m (given).

Now consider ΔABC, we have,

$\tan 60 = \frac{AB}{BC}$

$\implies \tan 60 = \frac{h}{50}$

$\implies \sqrt{3} = \frac{h}{50}$

Rearranging and simplifying,

$h=50\sqrt{3}$ m.

If we substitute $\sqrt{3}= 1.732$,

⇒ h ≈ 50×1.732

⇒ h ≈ 86.6 m.

Therefore, the height of the tree will be 50√3 m or about 86.6 m.