An anchor holding a boat stationary on a river forms a 65 degree angle with the river bottom. The anchor line is 40 meters long. Assuming the river has a uniform depth, how deep is the river directly below the boat?
what is 40Sin65? This is physics? Most folks would call this basic trig functions.
To find the depth of the river directly below the boat, we can use trigonometry. Let's call the depth of the river "d".
Here's a step-by-step explanation of how to find the depth of the river:
Step 1: Draw a diagram of the situation. Draw a right triangle, where the anchor line is the hypotenuse, the depth of the river is the opposite side, and the distance between the anchor and the boat is the adjacent side. Label the angle of 65 degrees and the length of the anchor line as 40 meters.
Step 2: Identify the trigonometric relationship that relates the angle and the lengths of the sides of a right triangle. In this case, we need to use the sine function, which relates the opposite side to the hypotenuse. Recall that sin(angle) = opposite/hypotenuse.
Step 3: Write down the equation using the identified trigonometric relationship. In this case, sin(65 degrees) = d/40 meters.
Step 4: Solve the equation for d. Rearrange the equation to isolate d: d = sin(65 degrees) * 40 meters.
Step 5: Use a calculator to find the value of sin(65 degrees) and then multiply it by 40 meters to find the depth of the river directly below the boat.
The answer will depend on the value of sin(65 degrees), but once you calculate it, you can multiply it by 40 meters to find the depth of the river.