A 60 foot antenna stands on top of a building. From a point on the ground, the angle of elevation to the top of the antenna measures 48 degrees and 39 degrees to the top of the building. How tall is the building?

This looks familiar, but I can't find the post where it was solved. So, here goes again:

If the distance from the building to the point on the ground is d, and the height of the building is h,

h/d = tan 39
(h+60)/d = tan 48

or,

d = h/tan 39 = (h+60)/tan 48
h/.8097 = (h+60)/1.1106
1.235h = .900h + 54.025
.335h = 54.025
h = 161.27

To find the height of the building, we can use the concept of trigonometry.

Let's assume the height of the building is "h" feet.

From the given information, we can form a right triangle with the antenna, the building, and the point on the ground where we are standing.

The angle of elevation to the top of the antenna is 48 degrees. This means that the opposite side of the angle (60 feet) is the height of the antenna.

The angle of elevation to the top of the building is 39 degrees. This means that the opposite side of the angle (h feet) is the height of the building.

Using the trigonometric ratio for tangent, we can write the following equation:

tan(48 degrees) = opposite side (60 feet) / adjacent side (ground distance in feet)

Re-arranging the equation, we get:

adjacent side (ground distance) = opposite side (60 feet) / tan(48 degrees)

Similarly, for the angle of elevation to the top of the building:

tan(39 degrees) = opposite side (h feet) / adjacent side (ground distance in feet)

Re-arranging the equation, we get:

adjacent side (ground distance) = opposite side (h feet) / tan(39 degrees)

Since the ground distance in both cases is the same, we can set the two expressions equal to each other:

opposite side (60 feet) / tan(48 degrees) = opposite side (h feet) / tan(39 degrees)

Now, let's solve this equation to find the height of the building (h):

h = (opposite side (60 feet) / tan(48 degrees)) * tan(39 degrees)

Using a scientific calculator, we can evaluate this expression to find the height of the building.