A cliff on the bank of a river is 300m high if angle of deprssion of a point on the oposite side of the river is 60 digree find the wigth of the river
ANSWER
RESUIT
To find the width of the river, we can use the trigonometric concept of angle of depression.
Let's consider the given situation:
1. The cliff is 300m high.
2. The angle of depression from the top of the cliff to the point on the opposite side of the river is 60 degrees.
To find the width of the river, we need to visualize the situation:
1. Draw a diagram with a river, a cliff with a point on top, and a point on the opposite side of the river.
2. Label the height of the cliff as 300m.
From the information given, we know that the angle of depression is 60 degrees. The angle of depression is the angle formed between the line of sight from the top of the cliff to the point on the opposite side of the river and the horizontal line.
We can apply basic trigonometry to find the width of the river. The opposite side of the triangle formed is the height of the cliff (300m), and the adjacent side is the width of the river that we need to determine.
Using the tangent function (tan), we can write the equation:
tan(angle of depression) = opposite/adjacent
Substituting in the given values:
tan(60 degrees) = 300/adjacent
Now, we can solve for the adjacent side (width of the river):
adjacent = 300 / tan(60 degrees)
Using a scientific calculator or trigonometric table, we can evaluate the tangent of 60 degrees:
tan(60 degrees) = 1.732
Substituting this value back into our equation:
adjacent = 300 / 1.732
Using a calculator, we calculate:
adjacent ≈ 173.21m
Therefore, the width of the river is approximately 173.21 meters.