Find the length of the missing sides in the triangle write your answers as integra's or as decimals rounded to the nearest tenth the diagram is not drawn to scale 7 y x + 45

This is a special right triangle called a 45-45-90 right triangle. you know this is the case because of the right angle symbol at the top and the 45 degree angle given. since triangles add up to 180 degrees, the other side must be 180 - 90 - 45 = 45 degrees.  we know that angles and sides must be proportionate so if two angles are the same, the lengths must also be the same. therefore, the lengths directly across from the 45 degree angles should be the same. thus, 7 and y are equal. y = 7.  you also need to know that in 45-45-90 triangles there is a special relationship where the sides of the triangle will have the relationship 1: 1: square root of 2 (or 1: 1: 1root2 which is the same thing). this can also mean x: x: xroot2. (where root = the square root of). i don't know how to enter a square root symbol on here so i used the word root to signify it.  therefore the sides of the triangle here are x: x: xroot2 or 7: 7: 7root2 which means 7 times the square root of 2. 7 times the square root of 2 = 9.9.  so the sides are 7, 7 and 9.9.  x = 9.9  y = 7

By the triangle sum theory, we can say that the other angle measures 45 degrees and of course the marked angle is measured 90 degrees so, we can prove that we are working with a 45-45-90 right triangle. because the base angles are equal, that tells us that it is an isosceles right triangle. opposite sides on an isosceles triangle are congruent. for that matter, y=7.to find x, use the pythagorean theorem. c²=a²+b²c is always the hypotenuse, a is the shorter leg and b is the longer leg. in that case a and b are equal so, it doesn't matter which one you put first. so, we can substitute.  x²=7²+7²x²=98² use the square root button on a calculator to take the square root off and find xx=9.=9.9y=7~have a great day♥

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