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 \(60^\circ\), find the width of...
Question 1 Report
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 \(60^\circ\), find the width of the river.
Answer Details
We can solve this problem using trigonometry. Let's draw a diagram of the situation:
A /| / | / | h = 300 m / | ----------- x B
Where point A is the top of the cliff, point B is the unknown point on the opposite side of the river, and x is the width of the river.
We know that the angle of depression from A to B is 60 degrees. This means that the angle of elevation from B to A is also 60 degrees.
Using trigonometry, we can set up the following equation:
tan(60) = h / x
where h is the height of the cliff and x is the width of the river. We can solve for x:
x = h / tan(60) x = 300 / √3 x = 100√3 meters
Therefore, the width of the river is 100√3 meters. Answer is correct.
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