A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of their line of sight from the ground to the top of the tower is 65°
? Round to the nearest hundredth.
To find the distance from the observer to the base of the tower, we can use trigonometry.
Let x be the distance from the observer to the base of the tower. Using the tangent function, we have:
tan(65°) = 200 / x
x = 200 / tan(65°)
x ≈ 82.47 feet
Therefore, the observer is approximately 82.47 feet away from the base of the tower.