Question

question 2 (mandatory) (1 point) saved
determine x to the nearest tenth of a metre.
4.6 m
77°
6.3 m
a) 7.5 m
b) 7.9 m
c) 6.9 m
d) 6.2 m

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(x^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 4.6\), \(b=6.3\), and \(C = 77^{\circ}\).

$$x^{2}=4.6^{2}+6.3^{2}-2\times4.6\times6.3\times\cos(77^{\circ})$$

Step2: Calculate each term

• \(4.6^{2}=21.16\)
• \(6.3^{2}=39.69\)
• \(\cos(77^{\circ})\approx0.2225\)
• \(2\times4.6\times6.3\times0.2225 = 2\times28.98\times0.2225=57.96\times0.2225\approx12.9\)

Step3: Substitute back

$$x^{2}=21.16 + 39.69-12.9$$

$$x^{2}=47.95$$

Step4: Find \(x\)

\(x=\sqrt{47.95}\approx6.9\)

Answer:

C. \(6.9\ m\)