Question

find the measure of angle a.
a = 7
b = 4
c = 8
a = ?°
round to the nearest tenth.

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \( b^{2}=a^{2}+c^{2}-2ac\cos A \).
We can rewrite it to solve for \(\cos A\): \(\cos A=\frac{a^{2}+c^{2}-b^{2}}{2ac}\).
Substitute \(a = 7\), \(b = 4\), and \(c = 8\) into the formula:
\(\cos A=\frac{7^{2}+8^{2}-4^{2}}{2\times7\times8}\)
\(=\frac{49 + 64-16}{112}\)
\(=\frac{97}{112}\approx0.866\)

Step2: Find the angle \(A\)

Since \(A=\cos^{-1}(\cos A)\), then \(A=\cos^{-1}(0.866)\)
Using a calculator, \(A\approx30.0^{\circ}\)

Answer:

\(30.0^{\circ}\)