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Lesechka [4]
3 years ago
8

A 45-45-90 triangle has a hypotenuse of length 7. What is the length of one of its legs? If necessary, round your answer to two

decimal places.
Mathematics
1 answer:
harkovskaia [24]3 years ago
4 0
If the legs are legnth x, then the hyptonuse is x√2

x√2=7
divide both sides by √2
x=7/√2
times (√2)/(√2)
(7√2)/2
3.5√2
aprox 4.94974
round
4.95
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m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS

m∠QRS = m∠RPQ + m∠PQR      {Exterior angle property of triangle}

4x - 15 = x +1 + x - 2

4x - 15 = x + x + 1-2          {Combine like terms}

4x - 15 = 2x - 1        {Subtract 2x from both sides}

4x - 2x - 15 = - 1

2x - 15 = - 1                  {Add 15 to both sides}

2x = -1 + 15

2x = 14          {Divide both sides by 2}

x = 14/2

x = 7

m∠RPQ = x + 1 = 7 + 1 = 8°

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