The value of a will be 3.0 cm. Then the correct option is C.
Let the triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c.
Then by the sine law, we have
[tex]\rm \dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]
Triangle ABC is shown.
Angle ∠CAB is 40 degrees and angle ∠ABC is 95 degrees.
The length of BC is a and the length of AC is 4.7 centimeters.
Then the third angle will be
∠A + ∠B + ∠C = 180°
40° + 95° + ∠C = 180°
∠C = 45°
Then by the sine law, we have
[tex]\rm \dfrac{\sin 40^o}{a} = \dfrac{\sin 95^o}{4.27} = \dfrac{\sin 45^o}{c}[/tex]
Then the value of a will be
sin 40° / a = sin 95° / 4.7
a = 3.0 cm
Then the correct option is C.
Learn more about law of sines here:
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