Question

solve for x.

Explanation:

Step1: Find the other non - right angle

The sum of angles in a triangle is \(180^{\circ}\). One angle is \(90^{\circ}\) and another is \(43^{\circ}\). Let the third angle be \(y\). Then \(y = 180-(90 + 43)=47^{\circ}\).

Step2: Use the sine rule

The sine rule states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here, if we consider the side of length \(22\) (opposite the right - angle, \(\sin90^{\circ}=1\)) and side \(x\) (opposite the \(47^{\circ}\) angle). So \(\frac{x}{\sin47^{\circ}}=\frac{22}{\sin90^{\circ}}\).
Since \(\sin47^{\circ}\approx0.731\) and \(\sin90^{\circ} = 1\), we have \(x=22\times\sin47^{\circ}\).
\(x\approx22\times0.731 = 16.082\approx16.0\)

Answer:

\(16.0\)