Pythagorean Theorem Finding The Length Of The Hypotenuse Math Wi Welcome to the pythagorean theorem: finding the length of the hypotenuse with mr. j! need help with the pythagorean theorem? you're in the right place!whethe. The pythagorean theorem states that if a triangle has one right angle, then the square of the longest side, called the hypotenuse, is equal to the sum of the squares of the lengths of the two shorter sides, called the legs. so if a a and b b are the lengths of the legs, and c c is the length of the hypotenuse, then a^2 b^2=c^2 a2 b2 = c2.
Pythagoras Theorem Example 1 Finding The Length Of The Hypotenuse Solution. the side opposite the right angle is the side labelled \ (x\). this is the hypotenuse. when applying the pythagorean theorem, this squared is equal to the sum of the other two sides squared. mathematically, this means: \ (6^2 8^2 = x^2\) which is the same as: \ (100 = x^2\) therefore, we can write:. Step 1: we assign the variables a = 5 and b = 12. step 2: next, we use the pythagorean theorem to find the length of the hypotenuse, c. c 2 = a 2 b 2 c 2 = 5 2 12 2 c 2 = 25 144 c 2 = 169 c. The hypotenuse is the longest side of the right triangle. it is located directly opposite the right angle of the triangle. most importantly, it is the quantity that is isolated by itself in the pythagorean theorem (equation 7.4.1). always isolate the quantity representing the hypotenuse on one side of the equation. 22. the lengths of two legs of a right triangle are 6 feet and 13 feet. find the length of the hypotenuse. round your answer to the nearest tenth. 23. the length of one leg of a right triangle is 4 meters, and the length of the hypotenuse is 8 meters. find the length of the other leg. round your answer to the nearest hundredth. 24.
How To Find The Length Of A Hypotenuse Using The Pythagorean Theorem The hypotenuse is the longest side of the right triangle. it is located directly opposite the right angle of the triangle. most importantly, it is the quantity that is isolated by itself in the pythagorean theorem (equation 7.4.1). always isolate the quantity representing the hypotenuse on one side of the equation. 22. the lengths of two legs of a right triangle are 6 feet and 13 feet. find the length of the hypotenuse. round your answer to the nearest tenth. 23. the length of one leg of a right triangle is 4 meters, and the length of the hypotenuse is 8 meters. find the length of the other leg. round your answer to the nearest hundredth. 24. 1. start with the formula: c = √ (a 2 b 2) don't forget: √ means square root and a 2 = a × a (a squared), b 2 = b × b. 2. find the lengths of the sides from the right triangle. in our example, the two shorter side lengths are a = 5 and b = 12. 3. substitute a = 5 and b = 12 into the formula. 8√13. correct answer: √89. explanation: because this is a right triangle, we can use the pythagorean theorem which says a2 b2 = c2, or the squares of the two sides of a right triangle must equal the square of the hypotenuse. here we have a = 5 and b = 8. a2 b2 = c2. 5 2 8 2 = c2. 25 64 = c2.
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