Question

At 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal. About how high is the building?

Answer 1

203 feet.

Explanation:

Please find the attachment.

Let h represent the height of the building.

We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.

We know that tangent relates opposite side of a right triangle to its adjacent side.

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

Upon substituting our given values in above formula, we will get:

`\text{tan}(35^(\circ))=(h)/(290)`

`290*\text{tan}(35^(\circ))=(h)/(290)*290`

`290*0.70020753821=h`

`h=290*0.70020753821`

`h=203.0601860809`

`h\approx 203`

Therefore, the building is approximately 203 feet high.