A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is 60º, find the width of the river?
A
100m
B
75√3 m
C
100√3m
D
200√3m
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Tan 60^\circ = \(\frac{300}{\text{x}}\)
x = \(\frac{300}{tan 60}\)
x = \(\frac{300}{\sqrt{3}}\)
x = \(\frac{300}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)
x = \(\frac{300\sqrt{3}}{3}\)
x = 100\(\sqrt{3}\)m
Source: Myschool Past Questions Archive (Record #9359)