A TV tower stands on top of the Empire State building. From a point (on the ground) 1150 feet from the base of the building, the angle of elevation to the top of the TV tower is 52 degrees. If the building is 1250 feet tall, what is the length of the TV tower?
(h+1250)/1150 = tan 52°
To find the length of the TV tower, we can use trigonometry and the given angle of elevation.
Let's call the length of the TV tower "x".
From the given information, we can form a right triangle with the TV tower as the vertical side, the distance from the base of the building to the point on the ground as the base, and the height of the building as the hypotenuse of the triangle.
Since the angle of elevation is the angle between the ground and the line of sight to the top of the TV tower, we have:
sin(52°) = x / 1150.
To solve for x, we can rearrange the equation:
x = sin(52°) * 1150.
Now, let's calculate the value of x:
x = sin(52°) * 1150.
= 0.7880 * 1150.
≈ 906.20.
Therefore, the length of the TV tower is approximately 906.20 feet.