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?

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) (Show Source): You can put this solution on YOUR website!
The length of each leg is .
That may be the expected answer.
You could also say that one of the legs is the base,
between angles measuring and ,
and the other leg is the height.
Then and
We know that and .

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 = length of the legs of the right isosceles triangle,
according to the Pythagorean theorem,

, but since we do not like seeing square roots in denominators, we rationalize,

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