Question

The angle of elevation of the sun is 39° from the ground. A business building downtown casts a shadow that is 89 m long. How tall is the building?​

Answer 1

`\tan 39 \textdegree = \displaystyle (h)/(89)\\\\89\tan 39 \textdegree = h\\\\h = 72`Answer:

72 m

Explanation:

Hi there!

Using the given information, we can construct a diagram. Please see the attached image.

We need to solve for the height of the building, or the length of the side opposite the angle that measures 39°. Given the only other piece of information is the length of its adjacent side, which is 89 m, we can use the tangent ratio to solve for the height:

`\tan \theta = \displaystyle (opposite)/(adjacent)`

Plug in the given values:

tan 39° = h/89

89 tan 39° = h

h = 72

Therefore, the height of the building is 72 m.

I hope this helps!