Question

solve the right triangle.
find the measure of \\( \angle b \\).
\\( m \angle b=60.0^{\circ} \\) (round to one decimal place as needed.)
the length \\( a \approx \\) units and the length \\( c \approx \\) units.
(round to one decimal place as needed.)

Explanation:

Step1: Find the length of side \(a\)

In a right - triangle, \(\tan A=\frac{a}{23}\). Given \(A = 30^{\circ}\), so \(a = 23\times\tan30^{\circ}\).
Since \(\tan30^{\circ}=\frac{\sqrt{3}}{3}\approx0.577\), then \(a = 23\times0.577\approx13.3\).

Step2: Find the length of side \(c\)

In a right - triangle, \(\cos A=\frac{23}{c}\). Given \(A = 30^{\circ}\), so \(c=\frac{23}{\cos30^{\circ}}\).
Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\approx0.866\), then \(c=\frac{23}{0.866}\approx26.6\).

Answer:

The length \(a\approx13.3\) units and the length \(c\approx26.6\) units.