A boat drops an anchor to the bottom of a lake. The anchor rope makes a 15 degree angle with the boat. The anchor rope is 24 feet long. How deep is the lake to the nearest foot?
Did you make your sketch?
If the depth is y
you should see that
h/24 = cos15°
h = 24cos15 = appr 23 ft
thank you! I guess I did it wrong
LOL, I would have had the 15 degrees from horizontal, living on the bleak ocean where at least a seven to one scope is required.
To find the depth of the lake, you can use trigonometry and the given information.
The angle between the anchor rope and the lake bottom is 90 degrees (since the anchor is dropped vertically).
We're given the length of the anchor rope, which is 24 feet, and the angle between the anchor rope and the boat, which is 15 degrees. We need to find the depth of the lake.
Using trigonometry, we can use the sine function to relate the angle and the length of the opposite side (depth of the lake) to the length of the hypotenuse (anchor rope).
sin(angle) = opposite / hypotenuse
In this case, sin(15 degrees) = depth of the lake / 24 feet.
To isolate the depth of the lake, we can multiply both sides of the equation by 24 feet:
depth of the lake = sin(15 degrees) * 24 feet.
Now we can calculate the depth using a calculator:
depth of the lake ≈ sin(15 degrees) * 24 feet ≈ 6.37 feet.
Therefore, the depth of the lake to the nearest foot is 6 feet.