A right triangle has a leg length of 10 meters and a hypotenuse that is 26 meters. What is the length of the other leg?

Answer:

The length of the other leg is 24 meters.

Step-by-step explanation:

Well, let's think about the equation that gives us the hypotenuse in the first place, the Pythagorean theorem (which only works on right triangles!).

[tex]a^2+b^2=c^2[/tex]

The a^2 is one side of the triangle that we know and the b^2 is the other, the c^2 is the hypotenuse we are trying to solve.

Seeing that in this question, we can put 10, in the place of a^2, and 26 in the place of c^2

[tex]10^2+b^2=26^2[/tex]

That's what we have down the information we have, but now we'll have to do some rearranging to solve for the other leg's length. First let's square the numbers, 10^2 = 100 and 26^2= 676!

[tex]100+b^2=676[/tex]

Now we need to get b^2 by itself so we can solve it! Let's subtract 100 from both sides to do so,

[tex]100-100+b^2=676-100[/tex]

[tex]b^2=676-100[/tex]

[tex]b^2=576[/tex]

Now we got b^2 = 576!

But that's not our answer we have to square root it to get rid of the squared part!

[tex]\sqrt{b^2} = \sqrt{576}[/tex]

and when we do that we get,

[tex]b=24[/tex]

The length of the other leg is 24 meters!

The length of the other leg is 24 m.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

A right triangle has a leg length of 10 meters and a hypotenuse that is

26 meters.

The length of the other leg = x

We will apply the Pythagorean theorem.

x² + 10² = 26²

x² + 100 = 676

x² = 676 - 100

x² = 576

x = 24

Thus,

The length of the other leg is 24 m.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

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