Notice that this is a right triangle with an acute angle that measures 30^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be 60^(∘). We will let the shorter leg of the triangle be s.
We found that the length of the shorter leg is sqrt(3). Moreover, in a 30^(∘)-60^(∘)-90^(∘) triangle the length of the longer leg is sqrt(3) times the length of the shorter leg. This will let us find the value of x.
Our second right triangle has an angle that measures 60^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle is 30^(∘). Remember, we already know that s=sqrt(3).
This triangle is also a 30^(∘)-60^(∘)-90^(∘) triangle. In this type of triangle, the length of the longer leg is sqrt(3) times the length of the shorter leg. This will let us find the value of y.
