Question

Given a right triangle, one leg is 10 in. and the hypotenuse is 15 in., find the length of the other leg using the Pythagorean theorem. Write your answer as a square root, not a decimal. (Use sq rt for the square root symbol).

Answer 1

We know that the Pythagorean Theorem is:\[c^{2}=a^{2}+b^{2}\] Since we know 'a' and 'c' we need to solve for 'b':\[b=\sqrt{c^{2}-a^{2}}\]

Now we can fill in know values and solve.

Answer 2

I dont know how to do the rest could you help me !!:)

Answer 3

Sure.

We know that 'c' is 15 and 'a' is 10 so:
\[b=\sqrt{15^{2}-10^{2}}\]

Can you go from here?

Answer 4

okay so 15(2)
is 225
and 10(2)
is 100
is the correct ?

Answer 5

Yes! Good so far

Answer 6

okay whats next ? do I subtract them ? and if yes how ?

Answer 7

So now you have:\[b=\sqrt{225-100}\]. If you subtract you get \[b=\sqrt{125}\]

Answer 8

This is usually good enough for the answer or you can simplify if required.

Answer 9

okay so i sqaure rooted 125 and i got 11 so is that goung to be my answer ?

Answer 10

\[\sqrt{125}=5\sqrt{5} \approx 11.18\]

All of them are correct, but the original question askes you to leave it in root form. So, the first one.

Answer 11

so 125

Answer 12

No not just 125. Square root 125

\[\sqrt{125}\]

Answer 13

ok so like this \[\sqrt{125}

Answer 14

Yes

Answer 15

okay thank you so much

Answer 16

You're welcome.