determine known length for a triangle one side is 2.5cm other side 1.6cm find how solve the third side
no way. There are lots of triangles with those two sides. If the 3rd side is x, all you know is that
2.5-1.6 < x < 2.5+1.6
To solve for the unknown length of the third side of a triangle, you can use the Pythagorean theorem or the Law of Cosines.
1. Using the Pythagorean theorem:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. However, if the triangle is not a right triangle, this theorem cannot be directly applied.
In your case, if the given triangle is a right triangle, you can use the Pythagorean theorem to solve for the unknown length of the third side.
Let's assume that the known side lengths are the two shorter sides of the triangle. In this case, the square of the length of the hypotenuse would be equal to the sum of the squares of the two known side lengths.
So, the formula to calculate the length of the hypotenuse (the unknown third side) is:
c = √(a^2 + b^2)
Where:
- c represents the length of the hypotenuse (unknown third side).
- a and b are the lengths of the known sides.
Substituting the given lengths into the formula, you can solve for the unknown length.
c = √(2.5^2 + 1.6^2)
c = √(6.25 + 2.56)
c = √8.81
c ≈ 2.97 cm
Therefore, the approximate length of the unknown third side is 2.97 cm.
2. Using the Law of Cosines:
The Law of Cosines can be used to solve for the unknown side length of any triangle, whether it is a right triangle or not. This law relates the lengths of the sides of a triangle to the cosine of one of its angles.
The formula to calculate the unknown side length using the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where:
- c represents the length of the unknown side.
- a and b are the lengths of the known sides.
- C is the angle opposite to the unknown side.
If the triangle is a right triangle, the angle opposite to the longest side (hypotenuse) is 90 degrees. In this case, to solve for the third side using the Law of Cosines, you can substitute the known side lengths and C = 90 degrees into the formula.
c^2 = 2.5^2 + 1.6^2 - 2 * 2.5 * 1.6 * cos(90)
c^2 = 6.25 + 2.56 - 8
c^2 ≈ 0.81
c ≈ √0.81
c ≈ 0.9 cm
Therefore, the approximate length of the unknown third side is 0.9 cm using the Law of Cosines.
Note: If the triangle is not a right triangle, you will need additional information, such as another angle or side length, to solve for the unknown length using the Law of Cosines.