Question

question 10 (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 } \\)
\\( \bigcirc \\) a) \\( \angle a = 46 ^ { \circ } \\)
\\( \bigcirc \\) b) \\( \angle a = 32 ^ { \circ } \\)
\\( \bigcirc \\) c) \\( \angle a = 51 ^ { \circ } \\)
\\( \bigcirc \\) d) \\( \angle a = 43 ^ { \circ } \\)

Explanation:

Step1: Apply the sine law

The sine law states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\).
So, \(\sin A=\frac{a\sin B}{b}\).
Substitute \(a = 3.3\), \(b = 6.2\), and \(B = 81^{\circ}\) into the formula:
\(\sin A=\frac{3.3\times\sin(81^{\circ})}{6.2}\).
Since \(\sin(81^{\circ})\approx0.9877\), then \(\sin A=\frac{3.3\times0.9877}{6.2}\).
Calculate \(3.3\times0.9877 = 3.25941\).
So, \(\sin A=\frac{3.25941}{6.2}\approx0.5257\).

Step2: Find the angle \(A\)

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

Answer:

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