A television tower stands on the top of the building from point 83.7 feet from the base of the building the angles of elevator to the top and the base of the tower are 63.20 minutes and 38.51 minutes respectively. How tall is the tower?

Draw a diagram.

height of building is b
height of tower is h

tan 63.20° = (b+h)/83.7
tan 38.51° = b/83.7

b = 83.7 * 0.796 = 66.6

(66.6+h)/83.7 = 1.980
h + 66.6 = 165.70
h = 99.1 ft

Hmmm. a 99ft tower on a 67ft building?

To find the height of the tower, we will use trigonometry and the given angles.

First, let's convert the angles from minutes to degrees.
Since there are 60 minutes in a degree, we divide the given angles by 60 to get the angles in degrees:

Angle to the top of the tower: 63.20 / 60 = 1.0533 degrees
Angle to the base of the tower: 38.51 / 60 = 0.6418 degrees

Now, we can use the tangent function to determine the height of the tower.

Let's assume the height of the tower is represented by 'h'. We can create a right triangle with the base of the triangle representing the distance from the base of the building to the tower (83.7 feet), the height representing the height of the tower (h), and the given angles.

Using the tangent function, we have:

tan(angle to the top of the tower) = h / distance from the base
tan(1.0533 degrees) = h / 83.7

Now, we can solve for 'h':

h = tan(1.0533 degrees) * 83.7

Similarly, for the angle to the base of the tower:

tan(angle to the base of the tower) = h / distance from the base
tan(0.6418 degrees) = h / 83.7

By solving for 'h' in the second equation, we get:

h = tan(0.6418 degrees) * 83.7

Finally, we can calculate the height of the tower by taking the average of the two values of 'h' we found:

Height of the tower = (h from first equation + h from second equation) / 2

Simply plug in the values and perform the calculations to find the height of the tower.