Find the value of x. Leave in fraction form.
3-6 right triangle
Show work please.
We can use the Pythagorean theorem to find the value of x in a 3-6 right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have the hypotenuse as 6 and one leg as 3.
So, using the Pythagorean theorem:
6^2 = 3^2 + x^2
Simplifying:
36 = 9 + x^2
Subtracting 9 from both sides:
27 = x^2
Taking the square root of both sides:
x = sqrt(27)
We can simplify this further:
x = sqrt(9*3)
x = 3sqrt(3)
Therefore, the value of x in a 3-6 right triangle is 3sqrt(3).