Question

1. solve for angle a.

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Here, \(a = 22\), \(b = 26\), \(c = 19\).
Substitute into the formula: \(22^{2}=26^{2}+19^{2}-2\times26\times19\times\cos A\).

Step2: Simplify the equation

Calculate the squares: \(484=676 + 361-988\cos A\).
Then \(484=1037-988\cos A\).
Rearrange to get \(988\cos A=1037 - 484\).
So \(988\cos A = 553\).

Step3: Solve for \(\cos A\)

\(\cos A=\frac{553}{988}\approx0.56\).

Step4: Find angle \(A\)

\(A=\cos^{-1}(0.56)\approx56^{\circ}\).

Answer:

\(A\approx56^{\circ}\)