Question

Match each value with its formula for ABC.

Answer 1

For the triangle ABC use the sine theorem:

$\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}$.

1. From $\dfrac{a}{\sin A}= \dfrac{b}{\sin B}$ you have $\dfrac{a}{b} \cdot \sin B=\sin A$.

2. From $\dfrac{b}{\sin B}= \dfrac{c}{\sin C}$ you have $\dfrac{b}{c} \cdot \sin C=\sin B$.

3. From $\dfrac{a}{\sin A}= \dfrac{c}{\sin C}$ you have $\dfrac{c}{a} \cdot \sin A=\sin C$.

4. From $\dfrac{a}{\sin A}= \dfrac{c}{\sin C}$ you have $\dfrac{\sin A}{\sin C} \cdot c=a$.

5. From $\dfrac{a}{\sin A}= \dfrac{b}{\sin B}$ you have $\dfrac{\sin B}{\sin A} \cdot a=b$.

6. From $\dfrac{b}{\sin B}= \dfrac{c}{\sin C}$ you have $\dfrac{\sin C}{\sin B} \cdot b=c$.

Answer 2

Answer:

1. sin A

2. sin B

3. sin C

4. a

5. b

6. c

Step-by-step explanation:

According to the Law of sine

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

1.

$\frac{\sin A}{a}=\frac{\sin B}{b}$

$\sin A=\frac{a}{b}\times \sin B$

The of first formula is sin A.

2.

$\frac{\sin B}{b}=\frac{\sin C}{c}$

$\sin B=\frac{b}{c}\times \sin C$

The of first formula is sin B.

3.

$\frac{\sin A}{a}=\frac{\sin C}{c}$

$\frac{c}{a}\times \sin A=\sin C$

The of first formula is sin C.

4.

$\frac{\sin A}{a}=\frac{\sin C}{c}$

$\frac{\sin A}{\sin C}\times c=a$

5.

$\frac{\sin B}{b}=\frac{\sin A}{a}$

$\frac{\sin B}{\sin A}\times a=b$

6.

$\frac{\sin C}{c}=\frac{\sin B}{b}$

$\frac{\sin C}{\sin B}\times b=c$

Therefore value of given formulas are sin A, sin B, sin C, a, b, c respectively.