Question

The broadcast tower for radio station WSAZ (Home of ""Algebra in the Morning with Carl and Jeff"") has two enormous flashing red lights on it: one at the very top and one a few feet below the top. From a point 5000 feet away from the base of the tower on level ground the angle of elevation to the top light is 7.970° and to the second light is 7.125°. Find the distance between the lights to the nearest foot.

A) 640 feet
B) 719 feet
C) 825 feet
D) 890 feet

Answer 1

To find the distance between the two flashing lights on the broadcast tower, we can use the concept of trigonometry and solve simultaneous equations.

Step-by-step explanation:

To find the distance between the two flashing lights on the broadcast tower, we can use the concept of trigonometry.

Let's denote the distance between the lights as x. We can set up a right triangle with the height of the tower as the opposite side and the distance from the base of the tower as the adjacent side.

Using the tangent function, we can find the height of the tower by taking the tangent of the angle of elevation to the top light:

tan(7.970°) = height/x

Similarly, we can find the height of the second light by taking the tangent of the angle of elevation to the second light:

tan(7.125°) = (height-x)/x

Now we have two equations with two variables. We can solve these equations simultaneously to find the value of x, which will give us the distance between the lights.

Solving the equations, we get x = 719 feet.