Question

the two triangles have at least two pairs of congruent corresponding angles, so the two triangles are similar by the angle - angle theorem. thus, the two triangles have the same ratio of height to width. the height - to - width ratio of each triangle is equal to i. the height - to - width ratio of each triangle is the of the line.

Explanation:

Step1: Identify height and width for first triangle

For the first triangle, height = 4000 and width = 2.

Step2: Calculate height - to - width ratio for first triangle

The ratio is $\frac{4000}{2}=2000$.

Step3: Identify height and width for second triangle

For the second triangle, height = 4000 and width = 3.

Step4: Calculate height - to - width ratio for second triangle

The ratio is $\frac{4000}{3}$. Since the triangles are similar, the height - to - width ratio of each triangle is equal to the ratio of the vertical change to the horizontal change (slope).

Answer:

2000 (using the first - triangle's values for the ratio calculation as an example; in general, for similar right - angled triangles formed by a line, the height - to - width ratio is the slope of the line)