Answer:
11 feet.
Explanation:
To find the number of feet in the height of a building that casts a shadow 32 feet long when the angle of elevation of the sun is 64°, we can use the tangent function and the fact that the tangent of an angle is equal to the opposite side divided by the adjacent side.
First, we need to determine the length of the shadow cast by the building when the angle of elevation of the sun is 90°, which is the same as the height of the building. We can do this using the formula for the tangent of an angle:
tan(64°) = opposite side / adjacent side
Since we know that the opposite side is 32 feet (the length of the shadow cast by the building), we can solve for the adjacent side:
adjacent side = opposite side / tan(64°)
= 32 feet / tan(64°)
We can find the value of tan(64°) using a calculator, which gives us a result of 2.81. Plugging this value into the formula above, we get:
adjacent side = 32 feet / 2.81
= 11.3 feet
Since the adjacent side is equal to the height of the building when the angle of elevation of the sun is 90°, we can say that the height of the building is 11.3 feet. Rounding this value to the nearest integer, we get:
Height of building = 11 feet
Thus, the height of the building is approximately 11 feet.