Use a trigonometric ratio to find the distance EF.

Mathematics

1 answer:

leonid [27]3 years ago

4 0

Answer:

The height of the building is approximately 73 m.

Step-by-step 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,

$\tan (\angle G)=\frac{EF}{FG}\\\tan 65\°=\frac{EF}{34}\\EF=34\times \tan 65\°=72.9\ m\approx 73\ m$

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

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