There are two(2) possible solutions for the given parameters of a triangle. Using the law of cosines, the parameters of the triangle are calculated.
The law of cosines is used to relate the angles and side lengths of a triangle.
They are given as follows:
a² = b² + c² -2bc cos(A)
b² = a² + c² - 2ac cos(B)
c² = a² + b² - 2ab cos(C)
The given triangle has B = 37°, a = 32 and b = 27
So, using the law b² = a² + c² - 2ac cos(B)
On substituting,
27² = 32² + c² - 2(32)c cos(37°)
⇒ c² - 50.56 c + 1024 = 729
⇒ c² - 50.56 c + 295 = 0
Since the obtained equation is quadratic, it has 2 solutions.
Using quadratic formula the solutions are calculated.
c = [50.56 ± [tex]\sqrt{50.56^2-4(1)(295)}[/tex]]/2(1)
On simplifying,
c = 43.8 and c = 6.7
Therefore, there are 2 possible solutions for the given triangle.
Learn more about the law of cosines here:
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