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 this triangle, let \(a = 13\), \(b = 18\), \(c = 19\). Then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 13\), \(b = 18\), \(c = 19\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

$$
LATEXBLOCK0
$$

Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(\cos A)\), then \(A=\cos^{-1}(0.7544)\approx40.9^{\circ}\)

Answer:

\(40.9\)