Question

A 12-m post supports a telephone pole that is leaning slightly towards it. The post makes an angle of 50° with the ground and meets the telephone pole at a point 9.5 m from its base. What is the measure of the angle closest to the post that the telephone pole makes with the ground?

Answer 1

The angle closest to the post that the telephone pole makes with the ground can be calculated using trigonometry.

Let's call the angle between the telephone pole and the ground **x**. Then, we can use the tangent function to find x:

tan(x) = (opposite side) / (adjacent side)

We know that the adjacent side is 9.5 m and that the angle between the post and the ground is 50 degrees. Therefore, we can calculate the opposite side as follows:

opposite side = adjacent side * tan(50 degrees)

opposite side = 9.5 m * 1.1918

opposite side = 11.32 m

Now we can use trigonometry again to find x:

tan(x) = opposite side / adjacent side

tan(x) = 11.32 m / 12 m

tan(x) = 0.9433

Taking the inverse tangent of both sides gives us:

x = tan^-1(0.9433)

x ≈ **40 degrees**

Therefore, the measure of the angle closest to the post that the telephone pole makes with the ground is **40 degrees**.