Answer: Let's use trigonometry to solve this problem. We can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle:
tan(theta) = opposite / adjacent
In this case, the opposite side is the height of the building, and the adjacent side is the length of the shadow. We know the length of the shadow is 69 ft, and we can calculate the angle of elevation using the fact that the sun is 56° above the horizon. Since the angle of elevation is measured from the ground up to the top of the building, we can use the complementary angle of 34° (90° - 56°) to solve for the height of the building:
tan(34°) = height / 69
Multiplying both sides by 69, we get:
height = 69 * tan(34°)
height ≈ 47.2
Rounding to the nearest tenth, we get the height of the building to be approximately 47.2 feet. Therefore, the height of the building is about 47.2 feet.
Explanation: