Question

A flag pole 18 feet tall casts a shadow 12 feet long at a specific time of day. Find, to the nearest degree, the angle of elevation of the sun at this time of day.

Answer 1

To find the angle of elevation of the sun, we can use the concept of similar triangles. The angle of elevation is approximately 56 degrees.

Step-by-step explanation:

To find the angle of elevation of the sun, we can use the concept of similar triangles. The flag pole, the shadow it casts, and the sun form a right triangle. The shadow is the adjacent side, the height of the flag pole is the opposite side, and the angle of elevation is the angle opposite the shadow.

Using the properties of similar triangles, we can set up the following proportion:

opposite / adjacent = height / shadow

Substituting the given values, we have (18 / 12) = (height / 12). Solving for height, we get height = 18. Therefore, the angle of elevation of the sun is the inverse tangent of the opposite/adjacent ratio, which is approximately 56 degrees.

Answer 2

56°

Step-by-step explanation:

Given that:

Height of flagpole = 18

Length of shadow = 12

The angle of elevation of tbe sun at the time of the day = θ

Uding trigonometry :

Tanθ = opposite / Adjacent

Tan θ = height of flagpole / length of shadow

Tan θ = 18 / 12

Tan θ = 1.5

θ = tan^-1 (1.5)

θ = 56.309

θ = 56° (nearest degree)