Question

12 college math

1. find the measure of the marked angle to the nearest degree. 3 marks

8.7 cm
6.8 cm
9.6 cm

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 6.8\), \(b=9.6\), \(c = 8.7\), and the marked angle be \(C\).
Substitute into the formula: \(8.7^{2}=6.8^{2}+9.6^{2}-2\times6.8\times9.6\times\cos C\).
Calculate \(8.7^{2}=75.69\), \(6.8^{2}=46.24\), \(9.6^{2}=92.16\).
So, \(75.69=46.24 + 92.16-130.56\cos C\).

Step2: Simplify the equation

First, simplify the right - hand side: \(46.24+92.16 = 138.4\).
The equation becomes \(75.69=138.4-130.56\cos C\).
Rearrange for \(\cos C\): \(130.56\cos C=138.4 - 75.69\).
\(130.56\cos C=62.71\).
Then \(\cos C=\frac{62.71}{130.56}\approx0.48\).

Step3: Find the angle

Take the inverse cosine: \(C=\cos^{-1}(0.48)\).
Using a calculator, \(C\approx61^{\circ}\).

Answer:

\(61^{\circ}\)