In a 30 ^(∘) - 60 ^(∘) - 90 ^(∘) triangle, the hypotenuse h is 2 times the length of the shorter leg s and the longer leg l is sqrt(3) times the length of the shorter leg.
Let's name the vertices of the given figure. Then we can find y and x, one at a time.
Finding x
We are given that ∠ABC is a right angle and that AB and BC are congruent. Therefore, △ ABC is a 45^(∘) - 45 ^(∘) - 90 ^(∘) triangle. We also know that the length of the hypotenuse AC is 13. By the 45^(∘) - 45 ^(∘) - 90 ^(∘) Triangle Theorem, we know the hypotenuse is sqrt(2) times the length of a leg, x.
13=sqrt(2)* x
To find x, let's solve the above equation.
We are given that ∠ABC is a right angle, and all of the sides in the polygon ABCD are equal. Therefore, the polygon is a square. Through the process of finding x, we know that the measure of ∠BAC and ∠ACB is 45 ^(∘).
Because polygon ABCD is a square, we know that ∠BAD is a right angle. Therefore, ∠CAD and ∠BAC are complementary. Knowing the measure of ∠BAC equals 45^(∘), we can find the value of y.
90=45+y ⇔ y=45
