Final Answer:
The length of the hypotenuse of a right triangle that are drawn from the vertices of the acute angles have lengths of 2, 13, and 73 is 146, However, the options provided (a, b, c, d) do not include 146.
Step-by-step explanation:
To solve this problem, we'll use a property of right triangles regarding the median to the hypotenuse.
This property states that the median drawn to the hypotenuse of a right triangle is exactly half the length of the hypotenuse.
Accordingly, the median to the hypotenuse would also be equal to the radius of the circle circumscribing the triangle.
Given that the medians from the acute angles have lengths of 2, 13, and 73, we can identify that the longest median, which is 73, is the median to the hypotenuse.
This median should be half the length of the hypotenuse because the hypotenuse is the longest side in a right triangle, and thus, its median would be the longest as well among the three medians mentioned.
Since the median to the hypotenuse is 73, we know that this is half the length of the hypotenuse. To find the length of the hypotenuse, we simply multiply the median length by 2:
Length of hypotenuse = 2 × Length of median to hypotenuse
= 2 × 73
= 146
Therefore, the hypotenuse is 146 units long. However, the options provided (a, b, c, d) do not include 146, so it appears there may be a misunderstanding with the question or the options themselves.
The problem statement or the options might not be presented correctly since none of the options match the calculated length of the hypotenuse.