Question

10.2 use law of cosines to
9 multiple choice 1 point
use the law of cosines. find m∠a to the nearest tenth of a degree.
examples:

1. find m∠c

7² = 11² + 6² - 2(11)(6)cosc
33.1°
77.4°
83.0°
85.2°

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). In \(\triangle ABC\), if we want to find \(\angle A\), the formula is \(BC^{2}=AB^{2}+AC^{2}-2(AB)(AC)\cos A\). Let \(BC = 14\), \(AB = 24\), \(AC = 25\). Then \(14^{2}=24^{2}+25^{2}-2\times24\times25\times\cos A\).

Step2: Simplify the equation

First, calculate the squares: \(196 = 576+625 - 1200\cos A\). Then \(196=1201 - 1200\cos A\).

Step3: Solve for \(\cos A\)

Rearrange the equation: \(1200\cos A=1201 - 196\). So \(1200\cos A = 1005\). Then \(\cos A=\frac{1005}{1200}=0.8375\).

Step4: Find the angle \(A\)

Take the inverse - cosine: \(A=\cos^{-1}(0.8375)\approx33.1^{\circ}\).

Answer:

\(33.1^{\circ}\)