A 60 ft. antenna stands on top of a building, From a point on the ground, the angles of elevation to the top and bottom of the antenna measure 58 and 44 respectively. How tall is the building

Triangle ABC, A the point of angle measurement on he ground, B the base of the antenna and C, the top of the antenna. Extend CB to ground level at D.

Angle CAB = 58 - 44 = 14º
Angle ACB = 32º
60/sin14 = AB/sin32
AB = 60sin32/sin14
h = BD = ABsin44º

To find the height of the building, we need to use trigonometry and the concept of angles of elevation.

Let's label the height of the building as 'h' and the distance from the point on the ground to the base of the building as 'x'.

We can create a right triangle with the antenna as the hypotenuse and the height of the building as the opposite side. The angle of elevation of 58 degrees is the angle between the hypotenuse and the opposite side (h). Similarly, the angle of elevation of 44 degrees is the angle between the hypotenuse and the adjacent side (x).

Using the tangent function, we can write two equations:
1) tan(58) = h/x
2) tan(44) = (h + 60)/x

Now, we can solve these equations simultaneously to find the values of h and x.

From equation 1, h = x * tan(58)

Substituting this value of h in equation 2, we get:
tan(44) = (x * tan(58) + 60)/x

Simplifying further, we get:
tan(44) = tan(58) + (60/x)
tan(44) - tan(58) = 60/x

Now, we can substitute the values of tan(44) and tan(58) which are approximately 0.965 and 1.619 respectively:
0.965 - 1.619 = 60/x

Solving this equation, we find:
-0.654 = 60/x

Cross multiplying, we get:
-0.654x = 60

Dividing both sides by -0.654, we find:
x ≈ -91.7

Since the distance cannot be negative, we discard this value.

Therefore, there is no valid solution to this problem. Please check the given angles again or provide additional information.