Question

right triangle (abc) has side lengths (ab = 7), (bc = 24), and (ac = 25). a second right triangle, (abc), has side lengths of 50, 14, and 48. find the ratio of the side opposite (angle a) to the hypotenuse of triangle (abc). use this ratio to identify the location of point (a) in the second right triangle. (1 point)
the ratio of the opposite side to the hypotenuse is 0.96, and point (a) is opposite the side that has length 14.
the ratio of the opposite side to the hypotenuse is 1.04, and point (a) is opposite the side that has length 48.
the ratio of the opposite side to the hypotenuse is 0.96, and point (a) is opposite the side that has length 48.
the ratio of the opposite side to the hypotenuse is 0.28, and point (a) is opposite the side that has length 14.

Explanation:

Step1: Identify opposite side to ∠A

In right - triangle \(ABC\), the side opposite \(\angle A\) is \(BC = 24\), and the hypotenuse is \(AC=25\).

Step2: Calculate the ratio

The ratio of the side opposite \(\angle A\) to the hypotenuse is \(\frac{BC}{AC}=\frac{24}{25}=0.96\).

Step3: Analyze the second triangle

In right - triangle \(A'B'C'\), we need to find the angle with the same ratio of opposite side to hypotenuse. If we consider the sides of lengths \(14\), \(48\), and \(50\), and assume the sides of the right - triangle follow the pattern of opposite, adjacent, and hypotenuse. The ratio of the side of length \(48\) to the hypotenuse of length \(50\) is \(\frac{48}{50} = 0.96\). So the angle opposite the side of length \(14\) will have the same trigonometric ratio as \(\angle A\) in triangle \(ABC\), and point \(A'\) is opposite the side that has length \(14\).

Answer:

The ratio of the opposite side to the hypotenuse is 0.96, and point \(A'\) is opposite the side that has length 14.