You can use the sine law for the given triangle to find the measure of a.
The value of a is given by
Option D: 3 cm
What is law of sines?
For any triangle ABC, with side lengths |AB| = c units, |BC| = a units, and |AC| = b units, then
[tex]\dfrac{sinA}{a} = \dfrac{sinB}{b} = \dfrac{sinC}{c}[/tex]
(If you draw it, you will notice that sin of an angle is sitting over the side length of its opposite side. This is the most important thing that people can mistake most commonly).
Using the above fact to calculate the measure of 'a' for the given context
We have these data
sin A = sin(40 degrees) = 0.643 approx
sin(b) = sin(95) degrees) = 0.996 approx
b = 4.7 cm
Using the first two inequalities, we get
[tex]\dfrac{sinA}{a} = \dfrac{sinB}{b} \\\\\dfrac{0.643}{a} = \dfrac{0.996}{4.7}\\\\a = \dfrac{0.643}{0.212} \approx 3 \: \rm cm[/tex]
Thus,
The value of a is given by
Option D: 3 cm
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