Question

19 multiple choice 2 points for the triangle shown below, find a if \\( \angle a = 55 ^ { \circ } \\) and \\( b = 13 \\). (round your answer to the nearest tenth.)

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan A=\frac{a}{b}\). Given \(A = 55^{\circ}\) and \(b = 13\), we can rewrite the formula as \(a=b\times\tan A\).

Step2: Substitute the values

Substitute \(A = 55^{\circ}\) and \(b = 13\) into the formula. We know that \(\tan(55^{\circ})\approx1.4281\). Then \(a = 13\times\tan(55^{\circ})\).

Step3: Calculate the value of \(a\)

\(a=13\times1.4281 = 18.5653\approx18.6\)

Answer:

\(18.6\)