Question

question 5 (mandatory) (1 point)
determine x to the nearest tenth of a metre.
4.6 m
77°
6.3 m
x
a) 7.9 m
b) 6.9 m
c) 6.2 m
d) 7.5 m

Explanation:

Step1: Apply the Law of Cosines

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

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

Step2: Calculate each term

First, \(6.3^{2}=39.69\), \(4.6^{2}=21.16\). And \(\cos(77^{\circ})\approx0.2225\). Then \(2\times6.3\times4.6 = 58.44\).

$$x^{2}=39.69 + 21.16-58.44\times0.2225$$

$$x^{2}=39.69+21.16 - 12.90$$

$$x^{2}=47.95$$

Step3: Solve for \(x\)

Take the square root of \(x^{2}\). \(x=\sqrt{47.95}\approx6.9\)

Answer:

B. \(6.9\ m\)