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The hypotenuse of a right triangle is 3 cm and one of the legs is 1 cm. What is the length of the other leg? Give an exact answer (that means do not use your calculator to get a decimal).

Respuesta :

musiclover10045
Using the Pythagorean theorem we can solve for the missing leg.

The equation  is a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. 

Filling in a and c with the information provided we will solve for b ( the missing leg).

1^2 + b^2 = 3^2

1 + b^2 = 9

b^2 = 9-1

b^2 = 8

b = SQRT(8)

b = 2 SQRT(2)

Answer:

The length of the other leg is [tex]2\sqrt{2}[/tex] cm.

Step-by-step explanation:

In a right triangle, if the length of two legs are [tex]a[/tex] and [tex]b[/tex], and the length of hypotenuse is [tex]c[/tex], then according to the Pythagorean theorem:   [tex]a^2+b^2= c^2[/tex]

Here, the hypotenuse is 3 cm and one of the legs is 1 cm. That means,  [tex]c= 3[/tex] and [tex]a=1[/tex]

Using the Pythagorean theorem.....

[tex](1)^2+b^2= (3)^2\\ \\ 1+b^2=9\\ \\ b^2=9-1\\ \\ b^2=8\\ \\ b=\sqrt{8}=\sqrt{4*2}=2\sqrt{2}[/tex]

So, the length of the other leg is [tex]2\sqrt{2}[/tex] cm.

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