Notice that this is a right triangle with an acute angle that measures 45^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must also be 45^(∘).
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 a and c.
Because, the legs in this type of triangle are congruent, the value of variable c is also 7.
Triangle 2
Our second 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 a=7.
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.
b= 2 * 7 ⇔ b=14
We found that the length of the hypotenuse is 14. 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 d.
d=sqrt(3) * 7 ⇔ d=7sqrt(3)
