Question

solve for a, rounded to the nearest tenth.
a = 17.8
a = 23.9
a = 21.5
a = 14.4

Explanation:

Step1: Find the value of angle \(b\)

In a right - triangle, the sum of the two non - right angles is \(90^{\circ}\). So \(b=90^{\circ}-42^{\circ} = 48^{\circ}\)

Step2: Use the tangent function

We know that \(\tan b=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan b=\tan48^{\circ}=\frac{a}{16}\)

Step3: Solve for \(a\)

Since \(\tan48^{\circ}\approx1.1106\), then \(a = 16\times\tan48^{\circ}\approx16\times0.9004\approx14.4\) (rounded to the nearest tenth)

Answer:

\(a = 14.4\)