The Chrysler Building casts a shadow approximately 130 feet long on the street when the Sun's rays form an 82.9 angle with the Earth. Approximately how tall is the building? Round you answer to four decimal places.

Question

The Chrysler Building casts a shadow approximately 130 feet long on the street when the Sun's rays form an 82.9 angle with the Earth. Approximately how tall is the building? Round you answer to four decimal places.

Answer 1

Let h=height of the building in feet

and θ=sun's angle with the horizontal = 82.9°
then
tan(θ)=h/130

Solve for h.

Answer 2

To find the height of the Chrysler Building, we can use the concept of shadow and similar triangles.

Let's label the height of the Chrysler Building as "h" and the length of the shadow as "s".

Since the Sun's rays form an 82.9-degree angle with the Earth, we can consider this angle as the angle of elevation from the top of the building to the tip of the shadow.

As the Sun's rays form a right angle with the ground, we have a right triangle formed between the height of the building, the length of the shadow, and the Sun's rays.

Using trigonometry, we can write the equation:

tan(82.9) = h / s

Now, let's solve this equation for h:

h = s * tan(82.9)

Substituting the given values, we have:

h = 130 * tan(82.9)

Using a calculator:

h ≈ 1178.0816

Therefore, the approximate height of the Chrysler Building is 1178.0816 feet. Rounded to four decimal places, the height is approximately 1178.0816 feet.