Answer: The measure of a is 6 units.
Step-by-step explanation:
Since we have given that
BC = a
AC = 8
BA = 11
∠A = 32.2°
Since we have two measures of sides and one measure of angle.
So, we can use "Law of Cosines ":
So, it becomes,
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}\\\\\cos 32.2^\circ=\dfrac{8^2+11^2-a^2}{2\times 11\times 8}\\\\0.846=\dfrac{64+121-a^2}{176}\\\\0.846=\dfrac{185-a^2}{176}\\\\0.846\times 176=185-a^2\\\\148.896=185-a^2\\\\a^2=185-148.896\\\\a^2=36.104\\\\a=\sqrt{36.104}\\\\a\approx 6[/tex]
Hence, the measure of a is 6 units.
