Question

The first day of the race will start with a bike race to Checkpoint 1; the straight-line distance to this checkpoint is 34 miles. The angle formed by the straight-line paths from START to Checkpoint 1 and START to Checkpoint 4 will be 32.2°. Determine a straight-line distance from checkpoint 4 to START so that the area of the triangular region complies with the local regulation of 200 - 250 square miles. Round your answer to one decimal place.

Answer 1

The distance from Checkpoint 4 to start is 28.8 miles

Step-by-step explanation:

Given that the distance from Start to Checkpoint 1 is 34 miles, and the angle formed by the straight-line paths from Start to Checkpoint 1 and Start to Checkpoint 4 is 32.2 degrees. Let x represent the side we want to find

Then we have:

`\cos 32.2=(x)/(34)`
`\begin{gathered} x=34\cos 32.2 \\ =28.77 \\ \approx28.8 \end{gathered}`