Question

To estimate the length of a lake, Caleb starts at one end of the lake and walks 95 m. He then turns and walks on a new path. which is 120∘ to the direction he was first walking in, and walks 87 m more until he arrives at the other end of the lake. Approximately how long is the lake? Round to the nearest tenths.

Answer 1

To estimate the length of the lake, we can use trigonometry. By using the sine function, we can find the second side of a right triangle formed by Caleb's walks. Adding the base walk to the second side walk gives us the approximate length of the lake.

Step-by-step explanation:

To estimate the length of the lake, we can use the concept of trigonometry. Let's assume that Caleb's initial walk forms the base of a right triangle, with the other two sides representing his subsequent walks. The angle between the base walk and the second walk is 120 degrees. We can use the sine function to find the length of the second side of the triangle: sin(120) = opposite/hypotenuse. Therefore, 87m = x/sin(120). Solving for x, we get x = 87m * sin(120) = approximately 75.4m.

To find the length of the lake, we add the base walk of 95m to the second side walk of 75.4m. Therefore, the approximate length of the lake is 95m + 75.4m = 170.4m. Rounding to the nearest tenth, the length of the lake is approximately 170.4m.