Since the right triangle has an acute angle that measures 45^(∘), by the Triangle Angle Sum Theorem the third angle must have a measure of 45^(∘). Let c be the length of the missing leg of the triangle.
Therefore, we have a 45^(∘)-45^(∘)-90^(∘)- triangle. In this type of triangle, the legs are congruent and the length of the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the length of the hypotenuse and missing leg.
b&= sqrt(2) * 6=6sqrt(2)
c&= 6
Let's add these newly found side lengths to the triangle.
Rectangle
Let's consider the given shape and the previously obtained information. Let s be the length of the bottom side of the rectangle.
Since opposite sides of a rectangle are congruent, we can conclude that s=8. We can find the value of a using the Segment Addition Postulate.
a=8+6 ⇔ a=14
