Which equation can be used to solve for c?
The Correct Answer and Explanation is:
Correct Equation:
c2=a2+b2c^2 = a^2 + b^2c2=a2+b2
This is the Pythagorean Theorem, where:
- c is the length of the hypotenuse (the side opposite the right angle),
- a and b are the lengths of the other two sides.
Explanation:
The equation c2=a2+b2c^2 = a^2 + b^2c2=a2+b2 is one of the most fundamental equations in geometry and is known as the Pythagorean Theorem. It applies specifically to right-angled triangles, where one of the angles is exactly 90 degrees.
In such a triangle, the side opposite the right angle is called the hypotenuse and is always the longest side. The equation helps us determine the length of this side (c) if we know the lengths of the other two sides (a and b). The formula works by squaring both of the known sides, adding those squared values together, and then taking the square root of the result to solve for c.
Mathematically, if you are given side a = 3 and side b = 4, you can plug them into the equation:c2=32+42=9+16=25c^2 = 3^2 + 4^2 = 9 + 16 = 25c2=32+42=9+16=25c=25=5c = \sqrt{25} = 5c=25=5
This demonstrates that if a triangle has side lengths of 3, 4, and 5, and one of its angles is 90 degrees, it satisfies the conditions of the Pythagorean Theorem.
This equation is not only used in geometry, but also in physics, engineering, architecture, and computer graphics — essentially anywhere distance calculation is needed. It forms the basis for calculating distance in coordinate geometry using the distance formula.
If you’re working on a different context (like algebraic equations or other applications), please provide more detail so I can tailor the explanation accordingly.
