Final answer:
To calculate the angle of elevation of the sun for a 20-foot building with a 55-foot shadow, we use the tangent function, resulting in an angle of approximately 19.98°.
Step-by-step explanation:
The question asks for the angle of elevation of the sun when a 20-foot-tall building casts a 55-foot long shadow. This problem can be solved using trigonometric ratios, specifically the tangent function, because the height of the building and the length of the shadow form a right-angled triangle with the angle of elevation (θ) being of interest. The tangent of an angle in a right-angled triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the length of the shadow.
To find the angle θ, we use the formula tan(θ) = opposite/adjacent, which in this problem translates to tan(θ) = 20/55. Using a calculator, we take the arctan (or inverse tangent) of 20/55 to find θ. After calculation, we get an angle of approximately 19.98°, which is the angle of elevation of the sun. The angle of the sun's elevation is important in various fields such as astronomy and geography and has practical applications in solar panel installation and architecture.