The side opposite the right angle is the hypotenuse. The Pythagorean theorem is used to solve for the length of the hypotenuse. If a right triangle has legs measuring a and b with hypotenuse c, the Pythagorean theorem is a² + b² = c².

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. Pythagorean Theorem: In a right triangle with hypotenuse c, a2+b2=c2.

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2 a 2 + b 2 = c 2 , which is known as the Pythagorean Theorem.

Example

1. Step 1 The two sides we know are Opposite (300) and Adjacent (400).
2. Step 2 SOHCAHTOA tells us we must use Tangent.
3. Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
4. Step 4 Find the angle from your calculator using tan-1

The formula is A2 + B2 = C2, this is as simple as one leg of a triangle squared plus another leg of a triangle squared equals the hypotenuse squared.

Note: In order for a2+b2=c2 to be true, the side length c must be the largest side length. So in order to test whether a triangle is right, you only need to plug in values where c is the largest among a,b,c.

a2 – b2 = (a + b)(a – b ) .

2 Answers

• Whereas a2−b2=(a+b)(a−b) is very simple, to factor a2+b2 requires the use of complex numbers.
• (a+ib)(a−ib)
• So a2+b2=(a+ib)(a−ib) , but there is no other factoring with real number coefficients.

Solution:- a2–b2 =(a+b)(a–b) – = ² – ² = +

It ended up very simple. And it is called the “difference of two squares” (the two squares are a2 and b2).

a2 + b2 = c2. This is known as the Pythagorean equation, named after the ancient Greek thinker Pythagoras. This relationship is useful because if two sides of a right triangle are known, the Pythagorean theorem can be used to determine the length of the third side.

BIG IDEA The square of a binomial a + b is the expression (a + b)2 and can be found by multiplying a + b by a + b as you would multiply any polynomials.

It’s true that you can’t factor A²+B² on the reals — meaning, with real-number coefficients — if A and B are just simple variables. So it’s still true that a sum of squares can’t be factored as a sum of squares on the reals.

where one perfect square is subtracted from another, is called a difference of two squares. It arises when (a − b) and (a + b) are multiplied together. This is one example of what is called a special product.

Factor the Sum of Perfect Cubes: a3 + b3 = (a + b)(a2 – ab + b2) Factor the Difference of Perfect Cubes: a3 – b3 = (a – b)(a2 + ab + b2) When trying to remember these patterns, remember that the first binomial term in the factored form in each pattern keeps the same sign as the sign between the perfect cubes.

A perfect square trinomial can be factored, so the equation can then be solved by taking the square root of both sides. Solve the equation x2 + 8x + 5 = 0 by completing the square. First, rewrite the equation in the form x2 + bx = c. Add the appropriate constant to complete the square, then simplify.

There are 31 perfect squares between 1 and 1000 (inclusive.)

So the first 20 square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 and 400.

You can also tell if a number is a perfect square by finding its square roots. Finding the square root is the inverse (opposite) of squaring a number. If you find the square root of a number and it’s a whole integer, that tells you that the number is a perfect square.