Question

find the measure of angle a.
a = 30
b = 15
c = 29
a =
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\).
Substitute \(a = 30\), \(b = 15\), and \(c = 29\) into the formula:
\(30^{2}=15^{2}+29^{2}-2\times15\times29\times\cos A\)
\(900=225 + 841-870\cos A\)
\(900=1066-870\cos A\)

Step2: Solve for \(\cos A\)

Rearrange the equation:
\(870\cos A=1066 - 900\)
\(870\cos A=166\)
\(\cos A=\frac{166}{870}\approx0.1908\)

Step3: Find the measure of angle \(A\)

Take the inverse cosine (\(\cos^{-1}\)) of \(0.1908\):
\(A=\cos^{-1}(0.1908)\approx79.0^{\circ}\)

Answer:

\(79.0^{\circ}\)