Question

A vertical light pole on a hillside casts a

shadow of 55 m long down the hill. If the
angle of elevation of the sun is 48.3° and the
angle of inclination of the hill is 21.4. Find
the height of the pole.

Answer 1

Answer:
`37.4\ m`

Explanation:

Given length of shadow
`l=55\ m`

Hill inclination
`21.4^(\circ)`

Angle of elevation for sun
`48.3^(\circ)`

Suppose the length of the pole is
`h`

from the figure, and using sine rule. It can written

`\Rightarrow (55)/(\sin 41.7^(\circ))=(h)/(\sin 26.9^(\circ))\\\\\Rightarrow h=55\cdot(\sin 26.9^(\circ))/(\sin 41.7^(\circ))\\\\\Rightarrow h=55\cdot 0.68011\\\Rightarrow h=37.40\ m`