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