Triangle ABC is a Right Triangle If AB=3 and AC=7 find BC. Leave your Answer in Simplest Radical Form.
Depends on which angle is the right angle.
If it is A, then BC = √58
If it is B, then BC = √40 = 2√10
since a big deal was made over Simplest Radical Form, I'd guess 2√10
Idk I am struggling with it too.
To find the length of BC in Triangle ABC, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Given that AB = 3 and AC = 7, we want to find BC.
Using the Pythagorean theorem, we have:
BC^2 = AB^2 + AC^2
BC^2 = 3^2 + 7^2
BC^2 = 9 + 49
BC^2 = 58
Taking the square root of both sides of the equation, we get:
BC = √58
Therefore, the length of BC is √58 in simplest radical form.
To find the length of BC in a right triangle ABC, we can use the Pythagorean theorem which 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 other two sides.
In this case, AB is one of the legs of the triangle and AC is the hypotenuse. Let BC be the other leg that we need to find.
According to the Pythagorean theorem:
AC^2 = AB^2 + BC^2
Substituting the known values:
7^2 = 3^2 + BC^2
49 = 9 + BC^2
Subtracting 9 from both sides:
40 = BC^2
To find BC, we take the square root of both sides:
√40 = √(BC^2)
Simplifying the square root:
√40 = BC
Breaking down 40 into its prime factors:
√(2^2 * 10) = BC
Simplifying further:
2√10 = BC
Therefore, the length of BC in simplest radical form is 2√10.