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
How do you draw the triangle to use to write it
w = 250 m / tan(50º)
To find the width of the river, we can use trigonometric ratios, specifically the tangent function. Here's how you can do it:
Step 1: Draw a diagram: Draw a right triangle, where the cliff is the vertical side and the width of the river is the horizontal side. The angle of depression is the angle between the horizontal side and the line of sight from the top of the cliff to the opposite side of the river.
Step 2: Identify the given information: We know that the cliff's height is 250m, and the angle of depression is 50 degrees.
Step 3: Identify the trigonometric ratio: The tangent function relates the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the height of the cliff, and the adjacent side is the width of the river.
Step 4: Apply the tangent function: The tangent of an angle is equal to the ratio of the opposite side to the adjacent side (tanθ = opposite/adjacent). Here, we have the opposite side as 250m, and we want to find the adjacent side, which is the width of the river. So, we can write the equation as follows: tan(50°) = 250m/width.
Step 5: Solve the equation: Rearrange the equation to solve for width. Multiply both sides of the equation by width: width * tan(50°) = 250m. Then, divide both sides by tan(50°) to isolate width: width = 250m / tan(50°).
Step 6: Calculate the width: Use a calculator to find the approximate value of the width. Plugging in the values, width = 250m / tan(50°) ≈ 250m / 1.1917 ≈ 209.99m.
Therefore, the width of the river is approximately 209.99 meters.