We will deal with these triangles one at a time. Let's start with the second one.
Triangle 2
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 5. 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 b.
b=sqrt(3)* 5 ⇔ b=5sqrt(3)
Triangle 1
The first right triangle has an angle that measures 30^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle is 60^(∘). Remember, we already know that b=5sqrt(3).
Once again, we have a 30^(∘)-60^(∘)-90^(∘) triangle. In this type of triangle, the length of the hypotenuse is twice the length of the shorter leg.
a= 2 * 5sqrt(3) ⇔ a=10sqrt(3)
We found that the length of the hypotenuse is 10sqrt(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 c.
