Question

question 3 (mandatory) (1 point)
determine \\( \angle a \\) to the nearest degree for the triangle with the given information
\\( a = 3.3 \mathrm{~m}, b = 6.2 \mathrm{~m}, \angle b = 81^{\circ} \\)

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 \(\sin A\approx0.5257\), then \(A=\sin^{- 1}(0.5257)\). Using a calculator, \(A\approx32^{\circ}\).

Answer:

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