find the angle of wlevation of the sun when a 12.5 meter tall telephone pole casts an 18 meter long shadow?

Draw a rt. triangle. The ver side is the telephone pole and the hor side is

the shadow.

tanA = 12.5/18 = 0.6944,
A = 34.8 Deg.

To find the angle of elevation of the sun, we can use the trigonometric function tangent (tan). Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side represents the height of the telephone pole and the adjacent side represents the length of the shadow cast by the pole.

Let's denote the angle of elevation as θ. We can use the formula for tangent:

tan(θ) = opposite/adjacent

In this case, the opposite side is the height of the telephone pole, which is 12.5 meters, and the adjacent side is the length of the shadow cast, which is 18 meters.

tan(θ) = 12.5/18

Now, we can solve for θ by taking the inverse tangent (arctan) of both sides:

θ = arctan(12.5/18)

Using a scientific calculator or an online calculator with the arctan function, we can find the value of θ.

Therefore, the angle of elevation of the sun when a 12.5-meter tall telephone pole casts an 18-meter long shadow is approximately θ degrees.

To find the angle of elevation of the sun, we can use the tangent of the angle. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the telephone pole (12.5 meters) and the adjacent side is the length of the shadow (18 meters).

So, the tangent of the angle of elevation (θ) can be calculated as follows:

tan(θ) = opposite/adjacent
tan(θ) = 12.5/18

Taking the inverse tangent (arctan or tan^-1) of both sides will give us the angle of elevation (θ):

θ = arctan(12.5/18)

Using a calculator, we find that arctan(12.5/18) is approximately 35.87 degrees.

Therefore, the angle of elevation of the sun is approximately 35.87 degrees.