A cliff on the bank of a river is 250m high if the angle of depression of the point of the opposite side of the river is 50 degree,find the width of the river
w/250 = cot50°
Where is the answer
To find the width of the river, we can use trigonometry. Specifically, we can use the tangent function.
Let's label the height of the cliff as "h" (given as 250m) and the angle of depression as "θ" (given as 50 degrees).
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the height of the cliff is opposite to the angle of depression, and the width of the river is adjacent to the angle of depression.
So, we have:
tan(θ) = opposite/adjacent
tan(50°) = h/width
We need to solve for the width, so rearranging the equation, we have:
width = h / tan(θ)
width = 250m / tan(50°)
Using a scientific calculator or math software, we can calculate the value of tan(50°) to be approximately 1.1918.
Plugging this value into the equation, we have:
width = 250m / 1.1918
Calculating this, we find that the width of the river is approximately 209.75m.