Answer: 13.8 m
Step-by-step explanation:
Given
From point A, angle of elevation is [tex]19^{\circ}[/tex]
From point B which is 18 m closer, it changes to [tex]32^{\circ}[/tex]
Suppose the height of tree is h
From figure, we can write
[tex]\Rightarrow \tan 32=\dfrac{h}{x}\\\\\Rightarrow h=x\tan 32^{\circ}[/tex]
Similarly
[tex]\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[/tex]
Deduce the value of h
[tex]\Rightarrow h=22.092\times \tan 32^{\circ}\\\Rightarrow h=13.8\ m[/tex]
Thus, the height of the tree is 13.8 m
