Question

Chidi measured the angle of elevation

of a tree and found it was 38°. He then
valked 25 m towards the tree and
measured the angle of elevation again
bo be 50°.
Find the actual height of the tree
d Find the total distance to the bot-
tom of tree from Chidi's initial
position
​

Answer 1

Answer: 56.72 m, 72.6 m

Explanation:

Given

The initial angle of elevation is
`38^(\circ)`

after walking 25 m, the angle of elevation is
`50^(\circ)`

In
`\triangle ABD`

`\Rightarrow \tan 38^(\circ)=(h)/(x+25)`

`\Rightarrow h=\tan 38^(\circ)(x+25)\quad \ldots(i)`

In
`\triangle ABC`

`\Rightarrow \tan 50^(\circ)=(h)/(x)\\\\\Rightarrow h=x\tan 50^(\circ)\quad \ldots(ii)`

From (i) and (ii)

`\Rightarrow x\tan 50^(\circ)=(x+25)\tan 38^(\circ)\\\Rightarrow 1.191x-0.781x=25* 0.781\\\Rightarrow 0.4104x=19.532\\\Rightarrow x=47.59\approx 47.6\ m`

`\Rightarrow h=47.6* \tan 50^(\circ)=56.72\ m`

The distance of tree bottom and Chidi's is

`\Rightarrow x+25=47.+25=72.6\ m`