A cliff on the bank of a river is 250m high if d angle of depression of d point of d opposite side of the river is 50 degree,find the width of d river
w = 250 m / tan(50º)
To find the width of the river, we can use trigonometry and the concept of angle of depression.
Let's assume that the width of the river is represented by the variable "x".
According to the given information, the angle of depression is 50 degrees. This angle is measured between a horizontal line (parallel to the riverbank) and the line of sight from the top of the cliff to the point on the opposite side of the river.
Now, we can use the tangent function (tan) to relate the angle of depression to the height of the cliff and the width of the river.
In a right-angled triangle formed by the cliff, the opposite side is the height of the cliff (250 meters) and the adjacent side is the width of the river (x).
The tangent of an angle can be determined by dividing the length of the opposite side by the length of the adjacent side.
Therefore, we can write the following equation:
tan(50°) = 250 / x
To find the value of x, we need to rearrange the equation:
x = 250 / tan(50°)
Using a scientific calculator, we can find the tangent of 50 degrees and plug it into the equation to evaluate the width of the river.