Example 1
Completion requirements
| Example 1 |
Determine the measure of angle \(A\), to the nearest degree.
Step 1: Write down what is given to determine whether to use the sine law or the cosine law.
\(a = 37\thinspace \rm{cm}\)
\(c = 125\thinspace \rm{cm}\)
\(\angle A = \thinspace ?\)
\(\angle B = 135^\circ\)
Because the third side of the triangle is unknown, the cosine law cannot be used. The sine law will work.
Step 2: Solve for angle \(A\).
\(\begin{align}
\frac{a}{{\sin A}} &= \frac{b}{{\sin B}} \\
\frac{{37}}{{\sin A}} &= \frac{{125}}{{\sin 135^\circ }} \\
\frac{{37\sin 135^\circ }}{{125}} &= \sin A \\
0.209... &= \sin A \\
\sin ^{ - 1} \left( {0.209...} \right) &= \angle A \\
12.081...^\circ &= \angle A \\
12^\circ &\doteq \angle A \\
\end{align}\)
\(a = 37\thinspace \rm{cm}\)
\(c = 125\thinspace \rm{cm}\)
\(\angle A = \thinspace ?\)
\(\angle B = 135^\circ\)
Because the third side of the triangle is unknown, the cosine law cannot be used. The sine law will work.
Step 2: Solve for angle \(A\).
\(\begin{align}
\frac{a}{{\sin A}} &= \frac{b}{{\sin B}} \\
\frac{{37}}{{\sin A}} &= \frac{{125}}{{\sin 135^\circ }} \\
\frac{{37\sin 135^\circ }}{{125}} &= \sin A \\
0.209... &= \sin A \\
\sin ^{ - 1} \left( {0.209...} \right) &= \angle A \\
12.081...^\circ &= \angle A \\
12^\circ &\doteq \angle A \\
\end{align}\)