To find the missing side of a triangle, you can use the Pythagorean theorem if the triangle is a right triangle or you can use the Law of Cosines if the triangle is not a right triangle.
1. For a right triangle:
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
The formula is:
a^2 + b^2 = c^2
Where:
- a and b are the lengths of the shorter sides
- c is the length of the longest side (the hypotenuse)
To find the missing side, you can rearrange the formula to solve for the missing side:
- If you are looking for the hypotenuse (c), take the square root of the sum of the squares of the other two sides: c = √(a^2 + b^2)
- If you are looking for one of the shorter sides (a or b), subtract the square of the known side from the square of the hypotenuse and then take the square root: a = √(c^2 - b^2) or b = √(c^2 - a^2)
2. For a non-right triangle:
If the triangle is not a right triangle, you can use the Law of Cosines to find the missing side. The Law of Cosines states that in a triangle with sides of lengths a, b, and c and angles A, B, and C opposite the corresponding sides, the following formula holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
This formula can be rearranged to solve for the missing side:
- To find side c, use the formula above.
- To find side a or b, you can rearrange the formula by solving for a^2 or b^2 and then taking the square root: a = √(c^2 + b^2 - 2bc * cos(A)) or b = √(c^2 + a^2 - 2ac * cos(B))
By using these formulas, you can find the missing side of a triangle whether it is a right triangle or not.
find the missing side of a triangle
1 answer