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 ∠A
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 to the hypotenuse of triangle ABC, we can use the equation sin(A) = opposite/hypotenuse. In this case, sin(A) = AB/CA = 6/10 = 0.6. Therefore, the ratio of the side opposite angle A to the hypotenuse is 0.6.
Using this ratio, we can locate point A' in the second right triangle. Since the hypotenuse of the second triangle is 40, the side opposite angle A' can be found by multiplying the ratio 0.6 by the hypotenuse, which gives us 0.6 * 40 = 24. Therefore, point A' is located opposite an angle whose side length is 24.