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

Answer:

203 feet.

Step-by-step 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:

$\text{tan}(35^{\circ})=\frac{h}{290}$

$290*\text{tan}(35^{\circ})=\frac{h}{290}*290$

$290*0.70020753821=h$

$h=290*0.70020753821$

$h=203.0601860809$

$h\approx 203$

Therefore, the building is approximately 203 feet high.