Find the value of x. Round the length to the nearest tenth. The diagram is not drawn to scale.

  2879.4 m

Step-by-step explanation:

The sine of an angle in a right triangle is the ratio of the side opposite to the hypotenuse. Here the interior angle at lower right is an "alternate interior angle" where the diagonal "transversal" crosses the parallel horizontal lines. Alternate interior angles are congruent, so the lower right interior angle is 10°. (Basically, the angle of elevation is equal to the angle of depression.)

Using the sine relation, we have ...

  sin(10°) = (500 m)/x

Multiplying by x/sin(10°) gives us the solution ...

  x = (500 m)/sin(10°)

  x ≈ 2879.4 m