Question

A surveyor uses indirect measurements to find the width of a river at a certain point.

The surveyor marks off 50 ft along the riverbank at right angles with the river and then sights an angle of 43° degrees to point A across the river, Find the width of the river. Round to hundredths. need help

Answer 1

The width of the river is approximately 46.63 ft, determined by using the tangent function in trigonometry with the provided angle of 43° and a baseline of 50 ft.

Step-by-step explanation:

To find the width of the river using indirect measurements, we utilize trigonometric functions.

Since the surveyor walks 50 ft along the riverbank, which is at right angles to the river, we have a right triangle where the 50 ft line is adjacent to the 43° angle, and the river's width is the opposite side.

We can use the tangent function, which relates the opposite side to the adjacent side in a right triangle.

The formula is as follows:

tan(angle) = opposite/adjacent

By inserting the values we have:

tan(43°) = width/50 ft

Now, we just solve for the width:

width = 50 ft * tan(43°)

Using a calculator, we find that:

width ≈ 50 ft * 0.932515086

= 46.63 ft

Therefore, the approximate width of the river is 46.63 ft when rounded to the hundredths place.