Final answer:
The length of the shadow cast by a 55ft tall building when the sun is 64 degrees above the horizon is approximately 26.8 feet, calculated using the tangent function in trigonometry and rounding to the nearest tenth.
Step-by-step explanation:
To find the length of the shadow cast by a 55ft tall building when the sun is 64 degrees above the horizon, we can use trigonometry. The relationship between the height of the building, the length of the shadow, and the angle of elevation of the sun can be described using the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.
The formula to find the length of the shadow (L) is:
L = height of the building / tan(angle of elevation)
Plugging in the given values:
L = 55ft / tan(64 degrees)
Using a calculator:
L = 55ft / 2.0503
L = 26.8186ft
Rounding to the nearest tenth gives us:
L ≈ 26.8 ft
Therefore, the length of the shadow cast by the building is approximately 26.8 feet.