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The other leg is 12 units long, am I right?
A^2+b^2 = c^2
first see the variable you know. We know the Hypotenuse (C) and one leg (A or B, we'll say it's A for this example)
Now take this and put it into the theorem above and you get
11^2 + B^2 = 15^2
now isolate B which means subtract the square of 11 (121) from the side that B is on and get b^2 = 15^2 + 11^2
which means B^2 = 225 +121
now add like terms (225 and 121) to get B^2 = 346
square root each side to get B = 18.60 (approximately) now you have the length of the other side.
Now put what you know into the formula for the area of a triangle which is A = 1/2BH
Area equals half the product of B and H. This formula only goes for A right triangle... I think... do the rest yourself good luck.
Sorry I did some of the work wrong but you get the idea, instead of subtracting 121 from 225 I added it but whatever I gave you the formula and operations you should be able to do it yourself :)