Example 2
Completion requirements
| Example 2 |
Determine the length, to the nearest foot, of the base of the roof truss depicted in the diagram.
Step 1: Write down what is given to determine whether to use the sine law or the cosine law.
\(a = 25\thinspace \rm{ft}\)
\(b = \thinspace ?\)
\(\angle A = 27^\circ\)
\(\angle C = 19^\circ\)
In order to use the cosine law, you must have at least two sides. Because only one side is known, the cosine law can be ruled out. Use the sine law.
Step 2: Determine the measure of angle \(B\).
\(\angle B = 180^\circ - 27^\circ - 19^\circ = 134^\circ\)
Step 3: Solve for \(b\).
\(\begin{align}
\frac{a}{{\sin A}} &= \frac{b}{{\sin B}} \\
\frac{{25}}{{\sin 27^\circ }} &= \frac{b}{{\sin 134^\circ }} \\
\frac{{25\sin 134^\circ }}{{\sin 27^\circ }} &= b \\
39.612... &= b \\
40 &\doteq b \\
\end{align}\)
The base of the truss is approximately \(40 \thinspace \rm{ft}\) long.
\(a = 25\thinspace \rm{ft}\)
\(b = \thinspace ?\)
\(\angle A = 27^\circ\)
\(\angle C = 19^\circ\)
In order to use the cosine law, you must have at least two sides. Because only one side is known, the cosine law can be ruled out. Use the sine law.
Step 2: Determine the measure of angle \(B\).
\(\angle B = 180^\circ - 27^\circ - 19^\circ = 134^\circ\)
Step 3: Solve for \(b\).
\(\begin{align}
\frac{a}{{\sin A}} &= \frac{b}{{\sin B}} \\
\frac{{25}}{{\sin 27^\circ }} &= \frac{b}{{\sin 134^\circ }} \\
\frac{{25\sin 134^\circ }}{{\sin 27^\circ }} &= b \\
39.612... &= b \\
40 &\doteq b \\
\end{align}\)
The base of the truss is approximately \(40 \thinspace \rm{ft}\) long.