Answer:
Triangle A:
- smaller leg = 3
- longer leg = 10
- hypotenuse = 10.4
Traingle B:
- smaller leg = 4
- longer leg = 13
- hypotenuse = 13.6
Triangle C:
- smaller leg = 5
- longer leg = 7
- hypotenuse = 8.6
Step-by-step explanation:
Let's find the distance of the legs for the 3 right triangles.
<u>Triangle A</u>
The smaller leg (SL) is from (2,5) to (2,8), so the length is given by the distance in the y-axis:
![SL_{A} = 8 - 5 = 3](https://tex.z-dn.net/?f=%20SL_%7BA%7D%20%3D%208%20-%205%20%3D%203%20)
Hence, the lenght of the smaller leg is 3.
The longer leg (LL) is from (-8, 8) to (2, 8), so the length is given by the distance in the x-axis:
![LL_{A} = 2 - (-8) = 10](https://tex.z-dn.net/?f=%20LL_%7BA%7D%20%3D%202%20-%20%28-8%29%20%3D%2010%20)
Then, the length of the longer leg is 10.
Now, we can find the hypotenuse (H) by using Pitagoras:
![H_{A} = \sqrt{SL_{A}^{2} + LL_{A}^{2}} = \sqrt{3^{2} + 10^{2}} = 10.4](https://tex.z-dn.net/?f=%20H_%7BA%7D%20%3D%20%5Csqrt%7BSL_%7BA%7D%5E%7B2%7D%20%2B%20LL_%7BA%7D%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B3%5E%7B2%7D%20%2B%2010%5E%7B2%7D%7D%20%3D%2010.4%20)
<u>Triangle B</u>
The SL is from (3, -9) to (7, -9)
The length of the SL is:
![SL_{B} = 7 - 3 = 4](https://tex.z-dn.net/?f=%20SL_%7BB%7D%20%3D%207%20-%203%20%3D%204%20)
The LL is from (7, -9) to (7, 4)
The length of the LL is:
![LL_{B} = 4 - (-9) = 13](https://tex.z-dn.net/?f=%20LL_%7BB%7D%20%3D%204%20-%20%28-9%29%20%3D%2013%20)
The hypotenuse is:
<u>Triangle C</u>
The SL is from (-10, -6) to (-10, -1)
The length of the SL is:
![SL_{C} = -1 - (-6) = 5](https://tex.z-dn.net/?f=%20SL_%7BC%7D%20%3D%20-1%20-%20%28-6%29%20%3D%205%20)
The LL is from (-10, -6) to (-3, -6)
The length of the LL is:
![LL_{C} = -3 - (-10) = 7](https://tex.z-dn.net/?f=%20LL_%7BC%7D%20%3D%20-3%20-%20%28-10%29%20%3D%207%20)
The hypotenuse is:
I hope it helps you!