Example 2
Completion requirements
| Example 2 |
Hank and Misty are travelling to the same place, but in different cars. Their cars are side by side on the Anthony Henday freeway in Edmonton. At one point, Misty gets stuck in a turn-off lane that exits the road at an angle of \(65^\circ\) to the Anthony Henday. After travelling \(5\) km each, how far apart are the two vehicles, to the nearest tenth of a kilometre?
Step 1: Draw a diagram.
Step 2: Solve for \(x\).
\(\angle A = 65^\circ\)
\(a = x\)
\(b = 5\thinspace \rm{km}\)
\(c = 5\thinspace \rm{km}\)
\(\begin{align}
a^2 &= b^2 + c^2 - 2bc\cos A \\
x^2 &= \left( 5 \right)^2 + \left( 5 \right)^2 - 2\left( 5 \right)\left( 5 \right)\cos 65^\circ \\
x^2 &= 28.869... \\
x &= 5.372... \\
x &\doteq 5.4 \\
\end{align}\)
Misty and Hank are approximately \(5.4\) km apart.
Step 2: Solve for \(x\).
\(\angle A = 65^\circ\)
\(a = x\)
\(b = 5\thinspace \rm{km}\)
\(c = 5\thinspace \rm{km}\)
\(\begin{align}
a^2 &= b^2 + c^2 - 2bc\cos A \\
x^2 &= \left( 5 \right)^2 + \left( 5 \right)^2 - 2\left( 5 \right)\left( 5 \right)\cos 65^\circ \\
x^2 &= 28.869... \\
x &= 5.372... \\
x &\doteq 5.4 \\
\end{align}\)
Misty and Hank are approximately \(5.4\) km apart.