Question

given the triangle
, find the length of side ( x ) using the law of sines. round your final answer to 4 decimal places.
( x = )
question help: video

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(C\). Then \(C = 180^{\circ}-29^{\circ}-28^{\circ}=123^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Here, if we assume the side opposite \(29^{\circ}\) is \(18\) (let \(a = 18\), \(A=29^{\circ}\)), and the side opposite \(28^{\circ}\) is \(x\) (let \(B = 28^{\circ}\), \(b=x\)). Then \(\frac{x}{\sin28^{\circ}}=\frac{18}{\sin29^{\circ}}\).

Step3: Solve for \(x\)

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Answer:

\(x\approx17.4320\)