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Ierofanga [76]
3 years ago
6

Three right triangles are drawn in the coordinate plane,

Mathematics
1 answer:
SashulF [63]3 years ago
5 0

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

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

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

<u>Triangle B</u>

The SL is from (3, -9) to (7, -9)

The length of the SL is:

SL_{B} = 7 - 3 = 4

The LL is from (7, -9) to (7, 4)

The length of the LL is:

LL_{B} = 4 - (-9) = 13

The hypotenuse is:

H_{B} = \sqrt{4^{2} + 13^{2}} = 13.6

<u>Triangle C</u>

The SL is from (-10, -6) to (-10, -1)

The length of the SL is:

SL_{C} = -1 - (-6) = 5

The LL is from (-10, -6) to (-3, -6)  

The length of the LL is:

LL_{C} = -3 - (-10) = 7

The hypotenuse is:

H_{C} = \sqrt{5^{2} + 7^{2}} = 8.6

I hope it helps you!

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Elena-2011 [213]

Answer: d=70; f=45; e=65

Step-by-step explanation:

NUMBER 1 WAY

110+d=180

      d=70

135+f=180

       f=45

d+f+e=180

70+45+e=180

            e=65

--------------------------------------------------

NUMBER 2 WAY

concept to know: exterior angle theorem

------------------------------

System of equation

d+e=135

f+e=110

d+e+f=180

------------------------

d=135-e

f=110-e

-------------------------

d+e+f=180

(135-e)+e+(110-e)=180

135-e+e+110-e=180

245-e=180

e=65

-----------------------

d=70

e=65

f=45

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