Question

The tower of a tower crane casts a shadow (on level ground) of 32 m when the sun is 55° above the horizon. what is the height of the tower?

Answer 1

45.7 meters.

Explanation:

Please see the attachment.

Let h be the height of the tower.

We have been given that tower of a tower crane casts a shadow (on level ground) of 32 m when the sun is 55° above the horizon.

We can see from our attachment that height of the tower will be opposite side to 55 degree angle and shadow of the tower is adjacent side to angle.

Since tangent relates the opposite and adjacent sides of a right triangle, so we will use tangent to find the height of the tower.

`\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

Upon substituting our given values we will get,

`\text{Tan }(55^o)=(h)/(32)`

`1.428148006742=(h)/(32)`

`32*1.428148006742=32*(h)/(32)`

`h=45.7007\approx 45.7`

Therefore, height of the tower is 45.7 meters.