Question

comparing angles of elevation and depression
a weather balloon is 529 meters above the ground. two weather stations, a and b, monitor the balloons progress.
compare the measures of the different angles of elevation and depression that are labeled in the diagram. which statements are true? check all that apply.
□ $x>y$
□ $v>x$
□ $w=y$
□ $y□ $v=w$
□ $x229m 347m

Explanation:

Step1: Relate angles via parallel lines

The horizontal dashed line is parallel to ground AB, so by alternate interior angles: $v = x$, $w = y$.

Step2: Compare triangle side lengths

In the right triangles formed by the balloon's vertical height (529m, common side):

• Station A is 229m from the vertical base, Station B is 347m from it. For right triangles with equal height, shorter adjacent side → larger acute angle.

Step3: Evaluate each statement

1. $x > y$: Since $v=x$, $w=y$, and $x$ corresponds to shorter adjacent side, $x>y$ is true.
2. $v > x$: $v=x$, so false.
3. $w = y$: Alternate interior angles, true.
4. $y < v$: $v=x$, $x>y$, so $y
5. $v = w$: $v=x$, $w=y$, $x≠y$, so false.
6. $x < w$: $w=y$, $x>y$, so false.

Answer:

• $x > y$
• $w = y$
• $y < v$