Its a 30-60-90 triangle

there's a line in the center that= 10

a. What is the length of the hypotenuse of triangle ABC?

b. What is the length of the shorter leg of triangle ABC?

c. What is the length of the longer leg of triangle ABC?

what is the relationship of "line in the center that= 10" to the sides of the triangle?

the line is going from the center of angle C to between AB. Its cutting the triangle down unevenly.

sorry its hard to explain. I wish i had the picture for you

To find the lengths of the hypotenuse and the legs of a 30-60-90 triangle, we need to understand the properties of this special type of triangle.

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The side lengths of the triangle can be determined based on this ratio.

a. To find the length of the hypotenuse (the side opposite the 90-degree angle in right triangle ABC), you need to multiply the length of the shorter leg by 2. In this case, the length of the shorter leg is 10, so the length of the hypotenuse is 10 * 2 = 20.

b. To find the length of the shorter leg, you can take one-third of the length of the hypotenuse. In this case, the length of the hypotenuse is 20, so the length of the shorter leg is 20 / 3 ≈ 6.67.

c. To find the length of the longer leg, you can multiply the length of the shorter leg by the square root of 3. In this case, the length of the shorter leg is 10, so the length of the longer leg is 10 * √3 ≈ 17.32.

So, the answers are:
a. The length of the hypotenuse is 20.
b. The length of the shorter leg is approximately 6.67.
c. The length of the longer leg is approximately 17.32.