Find the value of x. Round the length to the nearest tenth. The diagram is not drawn to scale.
A right triangle is drawn with the right angle in the lower left corner. A horizontal dashed line is drawn to the right from the top left vertex. The left vertical leg of the triangle is 500 meters. The hypotenuse is labeled x. The angle adjacent above the hypotenuse and adjacent below the horizontal line is 10 degrees.
To find the value of x, we can use trigonometry.
Since we know the length of the opposite side (500 meters) and the angle adjacent to it (10 degrees), we can use the tangent function:
tan(10°) = opposite / adjacent
tan(10°) = 500 / x
Solving for x:
x = 500 / tan(10°)
x ≈ 2860.2
Therefore, the value of x is approximately 2860.2 meters.