Question

Given: Triangle ABC is a right triangle. Line CZ is drawn perpendicular to the base AB. The length of CA is b, CB is a, AB is c, and CZ is h. Prove: ________.

1) Corresponding sides are proportional in similar triangles
2) Corresponding sides are proportional in similar triangles
3) The definition of the sine ratio
4) The definition of the sine ratio

Answer 1

In a right triangle, corresponding sides are proportional in similar triangles. The sine ratio is defined as the length of the opposite side divided by the length of the hypotenuse.

Step-by-step explanation:

In a right triangle, corresponding sides are proportional in similar triangles. This means that if two triangles are similar, then the ratios of corresponding sides will be equal. In the given triangle ABC and triangle CZB, we can see that they are similar because angle C is right. Therefore, we can conclude that the corresponding sides CA/CZ, CB/CZ, and AB/ZB are proportional.

The definition of the sine ratio states that for any angle in a right triangle, the sine ratio is equal to the length of the opposite side divided by the length of the hypotenuse. In the given triangle ABC, the angle ACB is the right angle, and the sides CA and CZ are the opposite side and hypotenuse respectively. Therefore, the sine ratio for angle ACB is CA/CZ = b/h.