Notice that this is a right triangle with an acute angle that measures 60^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be 30^(∘).
We found that the length of the shorter leg is 2sqrt(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 a.
Our second right triangle has an angle that measures 45^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle is also 45^(∘). Remember, we already know that a=6.
This triangle is a 45^(∘)-45^(∘)-90^(∘) triangle. In this type of triangle, both 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 values of b and d.
d & = 6
b &= sqrt(2) * 6 = 6sqrt(2)
