Question

a communications tower is attached to the top of a building. from a point, 10 meters from the base of the building, the angle of elevation to the top of the building is 60 degrees and the angle of elevation to the top of the tower is 68 degrees. what is the height of the communications tower, to the nearest tenth of a meter?

Answer 1

To find the height of the communications tower, set up a proportion using trigonometric functions and solve for the unknown height.

Step-by-step explanation:

To determine the height of the communications tower, we can use trigonometry and set up a proportion. Let's assume that the height of the building is h and the height of the tower is t.

From the given information, we can create two right triangles: one with the 60-degree angle of elevation to the top of the building and another with the 68-degree angle of elevation to the top of the tower.

Using the tangent function, we can set up the following proportion:
tan(60°) = h/10 and tan(68°) = (h + t)/10

Solving for t:
t = 10(tan(68°) - tan(60°))

Calculating the value, we find that the height of the communications tower is approximately 15.1 meters.