Answer
The measure of altitude the hiker gains is\[772\text{ feet}\].
Work Step by Step
Compute the measure of altitude the hiker gains as mentioned below:
\[\begin{align}
& \sin A=\frac{\text{Altitude}}{\text{Slope}} \\
& \sin 17{}^\circ =\frac{\text{Altitude}}{2640} \\
& \text{Altitude}=\sin 17{}^\circ \times 2640 \\
& \text{ = 772 feet}
\end{align}\]
