# A right triangle has a hypotenuse of length 30 and a leg of length 10. To the nearest tenth, what is the length of the other leg?

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We have the right angle triangle with sides:

The hypotenuse (h) = 30

One of the sides ( L) = 10

Find the other sides.

Let the other side be B:

Then we know that in a right angle triangle , the hypotenuse equals the square root of the sum of the sides squares:

==> hypotenuse^2 = side1^2 + side2^2

==> h^2 = L^2 + B^2

==> B^2 = h^2 - L^2

==> B = sqrt( h^2 - L^2)

= sqrt( 30^2 - 10^2)

= sqrt( 900 - 100)

= sqrt800

= 20sqrt2 *

Then, the length of the other sides is:

**B = 20sqrt2 = 28.3 ( to the nearest 10th)**

In a right angled triangle ABC, if B is the right angle, then Ac is the hypotenuse.

So by Pythagoras theorem, AB^2+BC^2 = AC ^2....(1)

Given AB = 10 and the hpotenuse AC = 30.

Therefore substituting the above values in eq(1), we get:

10^2+BC^2 = 30^2.

BC ^2= 30^2-10^2 = 900-100 = 800.

BC = sqrt(800) = sqrt(400*2) = 20 sqrt2.

BC = 20*1.4142 = 28.28 nearly

BC = 28.3 near to 10th place.