Question

The upper part of a tree is broken over by the wind makes an angle of 45° with the ground. If the horizontal distance from the root of the tree to the point,where the top of the tree meets the ground is 6m, then find the height of the tree.

Answer 1

SOLUTION

AD= 6m

$tan45 \degree = \frac{BA}{AB} \\ \\ = > 1 = \frac{BA}{6} \\ \\ = > BA = 6m \: \: \: \: \: [here \:, BC = BD] \\ \\ = > sin45 \degree = \frac{BA}{BD} \\ \\ = > \frac{1}{ \sqrt{2} } = \frac{6}{BD} \\ \\ = > BD= (6 \times 1.414)m \\ = > BD = 8.484m$

Now,

Height of the tree=AC = BA+BD

=) (6+8.484)m

=) 14.48m

Hope it helps ☺️