Question

There is an antenna on the top of a building. From a location 319 feet from the base of the building, the angle of elevation to the top of the building is measured to be 7°. From the same location, the angle of elevation to the top of the antenna is measured to be 5° more than the angle of elevation to the building. Find the height of the antenna. Round the height to the nearest 10th of a foot. No units necessary.

Answer 1

Explanation:

Let's call the height of the building "h", and the height of the antenna "a". From the given information, we have:

Angle of elevation to the top of the building = 7°

Angle of elevation to the top of the antenna = 7° + 5° = 12°

We can use tangent to find the height of the building and the height of the antenna. The tangent of an angle is equal to the height divided by the distance, so we have:

tan(7°) = h / 319

And

tan(12°) = (a + h) / 319

We can use the first equation to solve for h:

h = 319 * tan(7°)

And use the second equation to solve for a:

a = 319 * tan(12°) - h

Now that we have expressions for h and a, we can use the tangent function to find the values for h and a. We can use a calculator or look up the values in a table of tangent values.

Rounding the height of the antenna to the nearest 10th of a foot, we find:

a = 319 * tan(12°) - h = approximately 69.9 feet.