Question

given the triangle
, find the measure of angle a using the law of cosines.
picture is not drawn to scale
a =
degrees
give your answer accurate to at least one decimal place
question help: video

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). In a triangle with sides \(a = 22\), \(b = 20\), \(c = 30\), we can rewrite the formula for \(\cos A\) as \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 22\), \(b = 20\), \(c = 30\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

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Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(0.68)\), using a calculator, \(A\approx47.0\) degrees.

Answer:

\(47.0\)