Question

question 3 (mandatory) (1 point) saved
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} \\)

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

b) \\( \angle a = 45^{\circ} \\)

c) \\( \angle a = 43^{\circ} \\)

d) \\( \angle a = 51^{\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: \(\sin A=\frac{3.3\times\sin81^{\circ}}{6.2}\).
First, calculate \(\sin81^{\circ}\approx0.9877\). Then \(\sin A=\frac{3.3\times0.9877}{6.2}\approx\frac{3.2594}{6.2}\approx0.5257\).

Step2: Find the angle \(A\)

To find \(A\), take the inverse - sine (arcsin) of \(0.5257\). So \(A=\arcsin(0.5257)\).
Using a calculator, \(A\approx31.7^{\circ}\approx32^{\circ}\) (rounded to the nearest degree).

Answer:

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