Question

in right triangle abc, angle c is 90°. if bc is 15 and ac is 20, find angle a to the nearest degree. 40 39 37 38

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan A=\frac{BC}{AC}\). Given \(BC = 15\) and \(AC=20\), then \(\tan A=\frac{15}{20}=\frac{3}{4}\).

Step2: Use the inverse tangent function

We know that \(A=\tan^{- 1}(\frac{3}{4})\). Using a calculator, \(\tan^{-1}(0.75)\approx37^{\circ}\) (since \(\tan37^{\circ}\approx0.75\)).

Answer:

\(37\)