Question

How do you solve the right triangle given the Hypotenuse side is 7 and it is a 45-45-90 triangle?

Answer 1

The two catheti are equal and they measure `7/sqrt(2)`

Explanation:

If the two acute angles are equal, it means that the two catheti are also equal. If `c_1` and `c_2` are the two catheti and `h` is the hypothenuse, then Pitagora's theorem states that

`h^2=c_1^2+c_2^2`.

But in our case, `c_1=c_2`, so we have

`h^2=2c_1^2`, and thus

`c_1 = h/sqrt(2)`, since we can't accept negative solutions.