Final answer:
To find the angle of elevation of the sun, the tangent of the angle is calculated using the height of the tower and the length of its shadow. The ratio given by the height divided by the shadow length is equivalent to the tangent of a 60-degree angle, so the angle of elevation is 60 degrees. Option D is correct.
Step-by-step explanation:
The angle of elevation of the sun can be calculated by understanding the relationship between the height of the tower and the length of its shadow on the ground. In this scenario, we can use trigonometric functions, specifically the tangent, to find the angle of elevation. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side.
If the tower is 30 m high (opposite side) and casts a shadow of 10√3 m long (adjacent side), we can set up the equation as follows:
tan(θ) = opposite/adjacent
= 30 / 10√3
= 30 / (10 × 1.732)
= 30 / 17.32
= 1.732...
We recognize that 1.732 is the square root of 3, which corresponds to the tangent of a 60-degree angle. Therefore, the angle of elevation of the sun is 60 degrees.