SOLUTION: the hypotenuse of a right isosceles triangle is 5 cm long. Write an exact expression for the base and the height of the right triangle, useing primary trigonmetric ratios?

Algebra ->  Triangles -> SOLUTION: the hypotenuse of a right isosceles triangle is 5 cm long. Write an exact expression for the base and the height of the right triangle, useing primary trigonmetric ratios?       Log On


   

Question 827127: the hypotenuse of a right isosceles triangle is 5 cm long.
Write an exact expression for the base and the height of the right triangle, useing primary trigonmetric ratios?
Answer by KMST(5347) About Me  (Show Source):
You can put this solution on YOUR website!
The length of each leg is 5sqrt%282%29%2F2cm .
That may be the expected answer.
You could also say that one of the legs is the base,
between angles measuring 90%5Eo and 45%5Eo ,
and the other leg is the height.
Then base=hypotenuse%2Acos%2845%5Eo%29 and height=hypotenuse%2Asin%2845%5Eo%29
We know that cos%2845%5Eo%29=sqrt%282%29%2F2 and sin%2845%5Eo%29=sqrt%282%29%2F2 .

The length of the legs of the right isosceles triangle can also be calculated based on the Pythagorean theorem, without even mentioning trigonometric ratios.
If xcm= length of the legs of the right isosceles triangle,
according to the Pythagorean theorem,
x%5E2%2Bx%5E2=5%5E2
2x%5E2=5%5E2
x%5E2=5%5E2%2F2
x=sqrt%285%5E2%2F2%29%5D%5D%5D%0D%0A%7B%7B%7Bx=sqrt%285%5E2%29%2Fsqrt%282%29
x=5%2Fsqrt%282%29 , but since we do not like seeing square roots in denominators, we rationalize,
x=5sqrt%282%29%2F%28sqrt%282%29%2Asqrt%282%29%29
x=5sqrt%282%29%2F2