Question

find ab.
write your answer as an integer or as a decimal rounded to the nearest tenth.
ab =

Explanation:

Step1: Use trigonometric function

In right - triangle \(ABC\), \(\tan A=\frac{BC}{AB}\). Given \(A = 56^{\circ}\) and \(BC = 3\).

Step2: Rearrange the formula

We can rewrite the formula as \(AB=\frac{BC}{\tan A}\).

Step3: Substitute values

Substitute \(BC = 3\) and \(A = 56^{\circ}\) into the formula. \(\tan56^{\circ}\approx1.4826\). Then \(AB=\frac{3}{\tan56^{\circ}}\approx\frac{3}{1.4826}\approx2.1\).

Answer:

\(AB = 2.1\)