Question

Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

Answer 1

`x=5√(2)`

Explanation:

Right Triangle

It's the type of triangle that has an internal angle of 90°. The opposite side of this angle is called the hypotenuse and is the largest of all three. The other two sides (or legs) can be related to the hypotenuse and one of the internal angles with the use of the trigonometric ratios and the Pythagora's theorem.

A right triangle with an internal angle of 45° is also an isosceles triangle, in which case, both legs have the same length.

The Pythagora's theorem for this triangle states

`10^2=x^2+x^2`

Since it's an isosceles triangle. Operating

`2x^2=100`

`x^2=50`

Solving

`x=√(50)=5√(2)`

`\boxed{x=5√(2)}`