Question

determine ∠a to the nearest degree for the triangle with the given information. a = 3.3 m, b = 6.2m, ∠b = 81° a) ∠a = 32° b) ∠a = 46° c) ∠a = 43° d) ∠a = 51°

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). We can rearrange this formula to solve for \(\sin A\): \(\sin A=\frac{a\sin B}{b}\).
Substitute \(a = 3.3\), \(b = 6.2\), and \(B = 81^{\circ}\) into the formula: \(\sin A=\frac{3.3\times\sin(81^{\circ})}{6.2}\).
First, calculate \(\sin(81^{\circ})\approx0.9877\). Then, \(\frac{3.3\times0.9877}{6.2}=\frac{3.25941}{6.2}\approx0.5257\).

Step2: Find the angle \(A\)

Since \(\sin A\approx0.5257\), we find \(A\) by taking the inverse - sine (arcsin) of \(0.5257\). So, \(A=\arcsin(0.5257)\).
Using a calculator, \(A\approx32^{\circ}\).

Answer:

a) \(\angle A = 32^{\circ}\)