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

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines for finding an angle in a triangle with sides \(a\), \(b\), \(c\) and the angle \(A\) opposite side \(a\) is \(\cos(A)=\frac{b^{2}+c^{2}-a^{2}}{2bc}\). Let \(a = 23\), \(b = 18\), \(c = 22\). Then \(\cos(A)=\frac{18^{2}+22^{2}-23^{2}}{2\times18\times22}\).

Step2: Calculate the numerator

\(18^{2}=324\), \(22^{2}=484\), \(23^{2}=529\). So \(18^{2}+22^{2}-23^{2}=324 + 484-529=279\).

Step3: Calculate the denominator

\(2\times18\times22=792\).

Step4: Find the value of \(\cos(A)\)

\(\cos(A)=\frac{279}{792}\approx0.3523\).

Step5: Find the angle \(A\)

\(A=\cos^{- 1}(0.3523)\). Using a calculator, \(A\approx69.4^{\circ}\).

Answer:

\(69.4\)