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For the triangle ABC use the sine theorem:

[tex] \dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C} [/tex].

1. From [tex] \dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex] you have [tex] \dfrac{a}{b} \cdot \sin B=\sin A [/tex].

2. From [tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C} [/tex] you have [tex] \dfrac{b}{c} \cdot \sin C=\sin B [/tex].

3. From [tex] \dfrac{a}{\sin A}= \dfrac{c}{\sin C} [/tex] you have [tex] \dfrac{c}{a} \cdot \sin A=\sin C [/tex].

4. From [tex] \dfrac{a}{\sin A}= \dfrac{c}{\sin C} [/tex] you have [tex] \dfrac{\sin A}{\sin C} \cdot c=a [/tex].

5. From [tex] \dfrac{a}{\sin A}= \dfrac{b}{\sin B} [/tex] you have [tex] \dfrac{\sin B}{\sin A} \cdot a=b [/tex].

6. From [tex] \dfrac{b}{\sin B}= \dfrac{c}{\sin C} [/tex] you have [tex] \dfrac{\sin C}{\sin B} \cdot b=c [/tex].

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

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

1.

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]

[tex]\sin A=\frac{a}{b}\times \sin B[/tex]

The of first formula is sin A.

2.

[tex]\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

[tex]\sin B=\frac{b}{c}\times \sin C[/tex]

The of first formula is sin B.

3.

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]

[tex]\frac{c}{a}\times \sin A=\sin C[/tex]

The of first formula is sin C.

4.

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]

[tex]\frac{\sin A}{\sin C}\times c=a[/tex]

5.

[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]

[tex]\frac{\sin B}{\sin A}\times a=b[/tex]

6.

[tex]\frac{\sin C}{c}=\frac{\sin B}{b}[/tex]

[tex]\frac{\sin C}{\sin B}\times b=c[/tex]

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

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