Question

Environmentalist wants to measure the width of a river to monitor its erosion. From point A, she

ks downstream 100 feet and measures the angle from this point to point C to be 40.
a. How wide is the river? Round to the nearest tenth.

Answer 1

To calculate the width of the river, we can use trigonometry and set up a right triangle with the river's width as the unknown side, the distance downstream (100 feet) as the adjacent side, and the angle of 40 degrees as the opposite angle.

We can use the tangent function to solve for the width (w):

tan(40) = w/100

w = 100 tan(40)

Using a calculator, we get:

w ≈ 80.2 feet

So the width of the river is approximately 80.2 feet. Rounded to the nearest tenth, it would be 80.2 feet as well.