Question

A pole leans away from the sun at an angle of 9° to the vertical. When the elevation of the sun is 49°, the pole casts a shadow 43 ft long on level ground. How long is the pole?

Thanks

Answer 1

The pole is `40.4 ft` long.

Explanation:

Draw a sketch of the triangle which is formed. ensure that you know why the following angles are obtained.
The angle between the ground and the pole is `81°`
(The pole leans `9°` away from vertical.)

The angle at the end of the shadow of the pole is `49°`
(The angle of elevation of the sun.)

The distance on the ground is the length of the shadow and is `43 ft`.

The angle at the top of the pole is `50°`
There is a complete pair - an angle of `50°` and a side of length `43` and an incomplete pair - a known angle of `49°` and the unknown length of the pole `(x)`

Therefore we can use the Sin Rule

`x/(sin49°) = 43/(sin50°)`

`x = (43sin46°)/(sin50°)`

`x = 40.4 ft`