Triangle ABC is a right triangle. If AB = 3 and AC = 7, find BC. Leave your answer in simplest radical form.
To find the length of BC, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and AC) in a right triangle.
The Pythagorean theorem equation is: BC^2 = AB^2 + AC^2
We are given AB = 3 and AC = 7.
Plugging in the given values, we have:
BC^2 = 3^2 + 7^2
BC^2 = 9 + 49
BC^2 = 58
To find BC, we need to take the square root of both sides of the equation:
√(BC^2) = √58
BC = √58
Therefore, BC = √58 in simplest radical form.
Assuming the right angle is B, if the other side is x,
x^2 = 7^2-3^2