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.
Triangle A
The smaller leg (SL) is from (2,5) to (2,8), so the length is given by the distance in the y-axis:
[tex] SL_{A} = 8 - 5 = 3 [/tex]
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:
[tex] LL_{A} = 2 - (-8) = 10 [/tex]
Then, the length of the longer leg is 10.
Now, we can find the hypotenuse (H) by using Pitagoras:
[tex] H_{A} = \sqrt{SL_{A}^{2} + LL_{A}^{2}} = \sqrt{3^{2} + 10^{2}} = 10.4 [/tex]
Triangle B
The SL is from (3, -9) to (7, -9)
The length of the SL is:
[tex] SL_{B} = 7 - 3 = 4 [/tex]
The LL is from (7, -9) to (7, 4)
The length of the LL is:
[tex] LL_{B} = 4 - (-9) = 13 [/tex]
The hypotenuse is:
[tex] H_{B} = \sqrt{4^{2} + 13^{2}} = 13.6 [/tex]
Triangle C
The SL is from (-10, -6) to (-10, -1)
The length of the SL is:
[tex] SL_{C} = -1 - (-6) = 5 [/tex]
The LL is from (-10, -6) to (-3, -6)
The length of the LL is:
[tex] LL_{C} = -3 - (-10) = 7 [/tex]
The hypotenuse is:
[tex] H_{C} = \sqrt{5^{2} + 7^{2}} = 8.6 [/tex]
I hope it helps you!
