Answer: [tex]0.24\text{ radian}\ or\ 14^{\circ}[/tex]
Step-by-step explanation:
Given: A man is 6 feet 3 inches tall.
Since 1 feet = 12 inches
Therefore, 6 feet 3 inches=[tex]6\times12+3=36+3=39\ \text{inches}[/tex]
The top of his shadow touches a fire hydrant that is 13 feet 6 inches away.
Here, 13 feet 6 inches=[tex]13\times12+6=156+6=162\ \text{inches}[/tex]
Since the man is standing vertical to the ground, therefore he make right angle with the ground.
let x be the angle of elevation from the base of the fire hydrant to the top of the man's head.
We know that in a right triangle,
[tex]\tan x=\frac{\text{Perpendicular}}{\text{Base}}\\\Rightarrow\ \tan x=\frac{39}{162}\\\Rightarrow\ \tan x=0.240740\\\Rightarrow\ x=\tan^{-1}(0.24070)\\\Rightarrow\ x=0.2362445\approx0.24\text{ radian}\\=0.24\times\frac{180^{\circ}}{3.14}=13.5358\approx14^{\circ}[/tex]
