Right triangle ABC has side lengths AB = 6, BC = 8, and CA = 10. A
second right triangle has corresponding vertices of A', B', and C', with side lengths of 32, 40, and 24. In 3-5 sentences, describe how to find the ratio of the side opposite LA to the hypotenuse of triangle ABC. Then use this ratio to identify the location of point A' in the second right triangle.
To find the ratio of the side opposite angle A in triangle ABC to its hypotenuse, we can use the sine ratio. The sine of angle A is equal to the side opposite angle A divided by the hypotenuse. In this case, LA/10 = sine(A).
To find the location of point A' in the second right triangle, we can use the same ratio. The length of the side opposite angle A' would be the sine of A' multiplied by the hypotenuse. Therefore, LA' = 40 * sine(A').