Question

The University of Georgia 's football stadium, Sanford Stadium, installed a new scoreboards.

A football fan is sitting 320 feet from the scoreboard. When he is turned to face the
scoreboard, the angle of elevation to the bottom of the scoreboard is 7º and has angle of
elevation to the top of the scoreboard is 18°. What is the height of the scoreboard? Round
to the nearest foot.

Answer 1

To find the height of the scoreboard, we can use trigonometry and the given angles of elevation.

Step-by-step explanation:

To find the height of the scoreboard, we can use trigonometry and the given angles of elevation. Let's assume the height of the scoreboard is h. Since we have two angles of elevation, we can set up a trigonometric equation:

Tan(18°) = h / x (where x is the distance from the fan to the bottom of the scoreboard)

Similarly, Tan(7°) = (h + y) / x (where y is the height of the bottom of the scoreboard)

We know the distance x is 320 feet. Solving these two equations, we can find the value of h, which represents the height of the scoreboard.