The angle of elevation of the sun is 35 degrees at the time a pole casts a shadow of 150 m long. Find the height of the pole.

To solve this problem, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the pole) to the adjacent side (the length of the shadow).

The formula for tangent is:

tan(θ) = opposite/adjacent

We know that the angle of elevation (θ) is 35 degrees and the length of the shadow (adjacent) is 150 m. We want to find the height of the pole (opposite).

So we can set up the equation as follows:

tan(35) = height / 150

To solve for the height, we multiply both sides by 150:

height = 150 * tan(35)

Using a calculator, we find that tan(35) is approximately 0.7002.

So, the height of the pole is approximately 150 * 0.7002 = 105.03 m.

Therefore, the height of the pole is approximately 105.03 m.