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

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=(h)/(x)\\\\\Rightarrow h=x\tan 32^(\circ)`

Similarly

`\Rightarrow \tan19^(\circ)=(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=(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* \tan 32^(\circ)\\\Rightarrow h=13.8\ m`

Thus, the height of the tree is 13.8 m