Question

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. Given = 6"

Answer 1

From this detail that is a right isosceles triangle result that the angles from the base has measure of 45 degrees 
- there is given again that the length of legs is 6"
- than we drawn the height from the right angle on hypotenuse and use sin45 we get 
but we need to know that 6" = 6*2,6 = 15,6 cm = 0,156 m
cos 45° = (half of hypotenuse)/6"

sqrt2 /2 = (half of hyp) /6"

half of hyp. = 6"sqrt2 /2 = 3sqrt2" so than the length of hypotenuse will be 

equal 2*3sqrt2 = (6sqrt2)"