The distance between two docks on opposite sides of a river is 90 meters. The angle formed by the river bank and the line between the docks is 53°. What is the width of the river? Round your answer to the nearest meter and show your work.
w/90 = sin 53°
To find the width of the river, we can use trigonometry. Let's label the width of the river as "x."
We have a right triangle formed by the width of the river (x), the distance between the docks (90 meters), and the angle between the river bank and the line connecting the docks (53°).
In a right triangle, the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
Using this information, we can set up the equation as follows:
cos(53°) = x / 90
To solve for x, we can rearrange the equation:
x = 90 * cos(53°)
Now, let's calculate the value of x using a scientific calculator or trigonometric table:
x ≈ 90 * 0.6018
x ≈ 54.162
Rounding this answer to the nearest meter, the width of the river is approximately 54 meters.