Option B. Definition of sine in right triangle.
Step-by-step explanation:
In step 7: ΔBAE, [tex]AE=c sinB[/tex]
The answer is definition of sine in right triangle. Because, In a right angled triangle, the sine of an angle is equal to the length of the opposite side divided by hypotenuse.
By definition, [tex]\sin \theta=\frac{o p p}{h y p}[/tex]
Thus, [tex]\begin{aligned}\sin B &=\frac{A E}{c} \\c \sin B &=A E\end{aligned}[/tex]
Thus, the answer is definition of sine in right triangle.
In step 8: ΔCAE, [tex]AE=b sinC[/tex]
The answer is definition of sine in right triangle. Because, In a right angled triangle, the sine of an angle is equal to the length of the opposite side divided by hypotenuse.
By definition, [tex]\sin \theta=\frac{o p p}{h y p}[/tex]
Thus, [tex]\begin{array}{r}{\sin C=\frac{A E}{b}} \\{b \sin C=A E}\end{array}[/tex]
Thus, the answer is definition of sine in right triangle.
