Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 13 and hypotenuse labeled 16
square root of 425
square root of 3
square root of 29
square root of 87
To find the missing side in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, one leg of the triangle is labeled 13, and the hypotenuse is labeled 16. Let's label the missing side as x.
According to the Pythagorean theorem, we have:
x^2 + 13^2 = 16^2
x^2 + 169 = 256
To solve for x, we can subtract 169 from both sides:
x^2 = 87
Taking the square root of both sides, we get:
x = √87
So the length of the missing side in the triangle is the square root of 87.
Therefore, the correct answer is the square root of 87.