From a location on a bridge spanning a river, the angles of depression to the banks on either side are 30° and 45°. Given that the bridge is 50 meters above the banks, what is the width of the river?
Show answer & explanation
Correct answer: A
Explanation
Let the point on the bridge is 50 meters above the river bed.
Let x and y be the horizontal distances to the two banks, respectively.
For the angle of depression:
tan 30° = 50 / x ⇒ 1/√3 = 50 / x ⇒ x = 50√3
tan 45° = 50 / y ⇒ 1 = 50 / y ⇒ y = 50
Now the total width of the river = x + y
= 50√3 + 50
= 50(√3 + 1) meters