Question

Use a trigonometric ratio to find the distance EF.

A building casts a 34 m shadow when the Sun is at an angle of 25° to the vertical. How tall is the the
building to the nearest meter? Use a trigonometric ratio to find the distance FE.
250
Building
34 m
Shadow
The length EF is approximately

Answer 1

The height of the building is approximately 73 m.

Explanation:

The triangle EFG is shown below.

Given:

Length of shadow of building is,
`FG=34\ m`

Angle of inclination of Sun with the vertical is 25°.

Therefore, the angle of inclination of Sun with the horizontal is given as:

`\angle G=90-25=65\°`

Now, in triangle EFG as shown below, we use the tangent ratio to determine the height of building EF. Therefore,

`\tan (\angle G)=(EF)/(FG)\\\tan 65\°=(EF)/(34)\\EF=34* \tan 65\°=72.9\ m\approx 73\ m`

Therefore, the height of the building is approximately 73 m.