Question

A tower that is 120 feet tall casts a shadow 148 feet long. Find the angle of elevation of the sun to the nearest degree.

Answer 1

The angle of elevation of the sun is approximately 41.3 degrees.

Step-by-step explanation:

To find the angle of elevation of the sun, we can use the concept of similar triangles. We have a right triangle with the height of the tower as one side and the length of the shadow as the hypotenuse. Let's call the angle of elevation x.

Using the tangent function, we have:

tan(x) = height of tower / length of shadow

tan(x) = 120 ft / 148 ft

Using a calculator, we find:

x ≈ 41.3 degrees

Answer 2

To determine the angle of elevation of the sun for a 120 feet tall tower that casts a 148 feet long shadow, we apply the arctan function to the ratio of the tower's height to the shadow's length, which yields an angle of approximately 39 degrees.

Step-by-step explanation:

To find the angle of elevation of the sun, we can model the situation using a right-angled triangle where the tower is one side, the shadow is the base, and the angle of elevation is the angle between the base and the hypotenuse. The tower's height (120 feet) is the opposite side, and the shadow's length (148 feet) is the adjacent side in relation to the angle of elevation.

You can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. The formula tan(θ) = opposite/adjacent can be rearranged to find θ = arctan(opposite/adjacent).

θ = arctan(120/148) ≈ arctan(0.8108)

Using a calculator to find the arctan of 0.8108 will give us the angle in degrees.

θ ≈ 39 degrees (to the nearest degree)

Therefore, the angle of elevation of the sun is approximately 39 degrees.