Question

Mike wants to work out the height of a tree which has a fence around it. From A he sees that the angle of elevation of the top is 19° From B, 18m closer, the angle of elevation is 32° Workout the height of the tree

Answer 1

Answer: 13.8 m

Step-by-step explanation:

Given

From point A, angle of elevation is $19^{\circ}$

From point B which is 18 m closer, it changes to $32^{\circ}$

Suppose the height of tree is h

From figure, we can write

$\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}$

Similarly

$\Rightarrow \tan19^{\circ}=\dfrac{h}{x+18}\\\\\Rightarrow h=(x+18)\tan 19^{\circ}\\\text{Substitute the value of h}\\\Rightarrow x\tan 32^{\circ}=x\tan 19^{\circ}+18\tan 19^{\circ}\\\Rightarrow x(\tan32^{\circ}-\tan 19^{\circ})=18\tan 19^{\circ}\\\\\Rightarrow x=\dfrac{18\tan 19^{\circ}}{\tan32^{\circ}-\tan 19^{\circ}}\\\\\Rightarrow x=22.09\approx 22.1\ m$

Deduce the value of h

$\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m$

Thus, the height of the tree is 13.8 m