Question

A man who is 2m tall stands on horizontal ground 30m from a tree . The Angel of elevation of the top of the tree from his eyes is 28 . Fine the distance between the man eyes to the top of the tree

Answer 1

33.97 m

Explanation:

Given that,

The height of a man = 2 m

He stands on a horizontal ground 30m from a tree.

The angle of elevation of the top of the tree from his eyes is 28°.

We need to find the distance between the man eyes to the top of the tree. Let the height of the tree be h

Using trigonometry to find such that,

`\tan28=(h)/(30)\\\\h=\tan28* 30\\\\h=15.95`

Now let us consider that the distance between the man eyes to the top of the tree is x. Using Pythagoras theorem,

`x^2=30^2+15.95^2\\\\x=33.97\ m`

So, the distance between the man eyes to the top of the tree is 33.97 m.