Question

find the measure of angle c.
c = ?°
a = 55
b = 90
c = 50

Explanation:

Step1: Identify the triangle type and formula

This is a triangle with sides \(a = 55\), \(b = 90\), \(c = 50\). We can use the Law of Cosines to find angle \(C\). The Law of Cosines formula for angle \(C\) is: \(\cos(C)=\frac{a^{2}+b^{2}-c^{2}}{2ab}\)

Step2: Substitute the values

Substitute \(a = 55\), \(b = 90\), \(c = 50\) into the formula:

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Step3: Find the angle

Take the inverse cosine of \(0.8712\) to find \(C\):
\(C=\cos^{-1}(0.8712)\approx29.5^{\circ}\) (rounded to one decimal place)

Answer:

\(29.5\) (or depending on the required precision, could be approximately \(30^{\circ}\) if rounded to the nearest whole number)