Answer: 56.72 m, 72.6 m
Step-by-step explanation:
Given
The initial angle of elevation is [tex]38^{\circ}[/tex]
after walking 25 m, the angle of elevation is [tex]50^{\circ}[/tex]
In [tex]\triangle ABD[/tex]
[tex]\Rightarrow \tan 38^{\circ}=\frac{h}{x+25}[/tex]
[tex]\Rightarrow h=\tan 38^{\circ}(x+25)\quad \ldots(i)[/tex]
In [tex]\triangle ABC[/tex]
[tex]\Rightarrow \tan 50^{\circ}=\frac{h}{x}\\\\\Rightarrow h=x\tan 50^{\circ}\quad \ldots(ii)[/tex]
From (i) and (ii)
[tex]\Rightarrow x\tan 50^{\circ}=(x+25)\tan 38^{\circ}\\\Rightarrow 1.191x-0.781x=25\times 0.781\\\Rightarrow 0.4104x=19.532\\\Rightarrow x=47.59\approx 47.6\ m[/tex]
[tex]\Rightarrow h=47.6\times \tan 50^{\circ}=56.72\ m[/tex]
The distance of tree bottom and Chidi's is
[tex]\Rightarrow x+25=47.+25=72.6\ m[/tex]
