Question

1. determine the value of x. round to the nearest tenth. 5

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \( c^{2}=a^{2}+b^{2}-2ab\cos C\). In this triangle, let \(a = 36\), \(b=x\), \(c = 79 - 43=36\), and \(C = 112^{\circ}\).

$$x^{2}=36^{2}+36^{2}-2\times36\times36\times\cos(112^{\circ})$$

Step2: Calculate each term

First, \(36^{2}=1296\). Then, \(\cos(112^{\circ})\approx - 0.3746\).

$$x^{2}=1296 + 1296-2\times1296\times(-0.3746)$$

$$x^{2}=2592+2\times1296\times0.3746$$

$$x^{2}=2592 + 974.5$$

$$x^{2}=3566.5$$

Step3: Solve for \(x\)

Take the square - root of both sides: \(x=\sqrt{3566.5}\approx59.7\)

Answer:

\(x\approx59.7\)