Question

A man is 6 feet 3 inches tall. The top of his shadow touches a fire hydrant that is 13 feet 6 inches away. What is the angle of elevation from the base of the fire hydrant to the top of the man's head?

Answer 1

Answer:
`0.24\text{ radian}\ or\ 14^(\circ)`

Explanation:

Given: A man is 6 feet 3 inches tall.

Since 1 feet = 12 inches

Therefore, 6 feet 3 inches=
`6*12+3=36+3=39\ \text{inches}`

The top of his shadow touches a fire hydrant that is 13 feet 6 inches away.

Here, 13 feet 6 inches=
`13*12+6=156+6=162\ \text{inches}`

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,

`\tan x=\frac{\text{Perpendicular}}{\text{Base}}\\\Rightarrow\ \tan x=(39)/(162)\\\Rightarrow\ \tan x=0.240740\\\Rightarrow\ x=\tan^(-1)(0.24070)\\\Rightarrow\ x=0.2362445\approx0.24\text{ radian}\\=0.24*(180^(\circ))/(3.14)=13.5358\approx14^(\circ)`