Question

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find the value of x in the triangle shown below.
x =

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\) for a triangle with sides \(a,b,c\) and opposite angles \(A,B,C\) respectively.
In the given triangle, let the side of length \(4\) be opposite angle \(x\), and the side of length \(7.2\) be opposite the \(32^{\circ}\) angle.
So, \(\frac{4}{\sin x}=\frac{7.2}{\sin32^{\circ}}\)

Step2: Solve for \(\sin x\)

Cross - multiply: \(4\times\sin32^{\circ}=7.2\times\sin x\)
\(\sin x=\frac{4\times\sin32^{\circ}}{7.2}\)
We know that \(\sin32^{\circ}\approx0.5299\)
\(\sin x=\frac{4\times0.5299}{7.2}\)
\(\sin x=\frac{2.1196}{7.2}\approx0.2944\)

Step3: Find \(x\)

Take the inverse - sine of \(0.2944\), \(x = \sin^{-1}(0.2944)\)
Using a calculator, \(x\approx17^{\circ}\)

Answer:

\(17\)