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'Unit 8: right triangles and trigonometry Homework 2: special right triangles HELP PLEASE!! X= y = 6 X 25-3 608 X = y ='
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Name Proof of the Pythagorean Theorem and its Converse - Matching Worksheet Write the letter of the answer that matches the problem. 1. A triangle has sides with lengths of 21 miles 28 miles and 35 miles. Is it a right triangle a* 2. Calculate the height of a triangle with sides at lengths of 15 feet 39 feet. b. 3. State true if triangle is a right triangle that has sides with lengths of 24 kilometers 45...
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Welcome to the NIT website and math podcast my name is Vanessa, and today I'll be covering the Thackeray and theorem, and it's converse so what does the Pythagorean theorem actually state it basically just makes a fact about the character especial characteristics of the right triangle a right triangle is obviously a triangle that contains a ray angle or a 90-degree angle within it and the longest side or the side opposite that 90-degree angle is what's called the hypotenuse so if you draw out a right triangle feel a right angle here all right this is our ninety-degree angle the opposite side opposite that right angle is what's called the hypotenuse and the other two sides which are a way from the hypotenuse are called the legs, so it's this one and this one, and they're both called legs now what the Pythagorean theorem states about the characteristics of bringing all these together is saying that the if you were to square the length of the hypotenuse it's going to be equal to the sum of the square of both the legs so to put that in an equation type of form is if we were to call the legs a and B and call the hi pot and give the length of the hypotenuse C it's basically saying that the if the square of both the legs the sum of the square of both the legs is equal to the square of the hypotenuse and that's what the Pythagorean theorem and equation try to tell you if we try to do an example based on this theorem so say if a problem tells us that we have a right triangle that has legs of length 3 and 4 find the hypotenuse so if we were to rewrite our Pythagorean theorem equation a squared plus B squared is equal to C skirt and the problem tells us that we have leg two legs of length three and four we want to fill in a and B with three and four because those the Bambi are the variables that represent the legs, so we have 3 squared plus 4 squared is equal to C squared, and then we'll just solve for C so 3 squared is 9 4 squared is 16 equals C squared 9 plus 16 is 25 is equal to C squared, and then we take the square root of both sides to get rid of squared, and we get 5 now keep in mind though that technically when you do take the square root of a number you get both positive and negative but because we're talking about the lengths of triangle you can only have a positive length which is why I just stuck with positive 5 as my answer, so that was that no I'm just rated for an example say if the problem said that one of the lengths was 15th of a leg and the hypotenuse is 39, and then they asked you to find the length of the second leg so again let's rewrite our equation a squared plus B squared is equal to C squared now they're telling us one of the legs is 15 so let me just pick a pick B is her is that leg so 15 squared, and they're telling us the hypotenuse is 39 the length of the hypotenuse is 39 so let's put that in here so C's our hypotenuse so 39 squared, and they want to spawn what the other leg is so our variable in this case is a so let's solve...