Question

question 2 of 10
the measure of θ, in degrees, is approximately 48.8°.
a. true
b. false

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In the triangle, let \(a = 5.3\), \(b = 4\), \(c = 7\), and \(C=\theta\). Then \(7^{2}=5.3^{2}+4^{2}-2\times5.3\times4\times\cos\theta\).

Step2: Simplify the equation

\(49 = 28.09+16 - 42.4\cos\theta\).
\(49=44.09 - 42.4\cos\theta\).
\(49 - 44.09=- 42.4\cos\theta\).
\(4.91=- 42.4\cos\theta\).
\(\cos\theta=\frac{4.91}{- 42.4}\approx - 0.1158\).
\(\theta=\cos^{-1}(-0.1158)\approx96.66^{\circ}
eq48.8^{\circ}\).

Answer:

B. False