Question

The upper part of tree broken by wind makes an angle of ${45}^{\circ }$ with the ground and horizontal distance from the foot of the tree to the point where the top of tree touches the ground is $12$ m, find the height of tree before it was broken ?

Answer 1

$AC$ is the broken part of the tree and $AB$ is the remaining part of the tree.

We get a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle.

We get $AB=BC=12$m

${AC}^2={AB}^2+{BC}^2$

$\Rightarrow {AC}^2={12}^2+{12}^2=2\times {12}^2$

$\Rightarrow AC=12\sqrt{2}$m

Height of the tree$=$broken part$+$ remaining part

$AC+AB=12+12\sqrt{2}=12(1+\sqrt{2})$