Pythagorean Theorem Derivation. Consider a right-angled triangle ΔABC. From the below figure, it is right-angled at B. Let BD be perpendicular to the side AC. From the above-given figure, consider the ΔABC and ΔADB, In ΔABC and ΔADB, ∠ABC = ∠ADB = 90°. ∠A = ∠A → common.

The Pythagorean Theorem If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This relationship is represented by the formula:

This formula is the law of cosines, sometimes called the generalized Pythagorean theorem. From this result, for the case where the radii to the two locations are at right angles, the enclosed angle Δ θ = π /2, and the form corresponding to Pythagoras's theorem is regained: s 2 = r 1 2 + r 2 2 . {\displaystyle s^{2}=r_{1}^{2}+r_{2}^{2}.}

The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared. You might recognize this theorem in the form of the Pythagorean equation: a 2 + b 2 = c 2.

9 2 + x 2 = 10 2 81 + x 2 = 100 x 2 = 100 − 81 x 2 = 19 x = 19 ≈ 4.4. Problem 3. Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest hundredth. Remember our steps for how to use this theorem. This problems is like example 2 because we are solving for one of the legs . Show Answer.