Erica is participating in a road race. The first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25
∘ north of east. The road then turns due north for another 3.0 mi to the finish line. In miles, what is the straight-line distance from the starting point to the end of the race? Express your answer in miles.
1 answer:
Answer:
6.79 miles
Step-by-step explanation:
Consider the triangle ABC attached where A is the starting point and C is the finish point.
|AB|=5.2 miles
|BC|=3.0 Miles
≺ABC = 90+75 =165°
We are given the length of two sides and an angle not opposite any of the given sides.
The rule for solving this scenario is referred to as the Cosine Rule.
Note that the side opposite each angle is labelled using the corresponding small letter.
The Cosine Rule States that:
b²=a²+c²-2acCosB
|AC|²=3²+5.2²-(2X5.2XCos165°)
|AC|²=9+27.04-(-10.05)
|AC|²=9+27.04+10.05=46.09
|AC|=√46.09=6.79 miles
Therefore the distance on a straight line from A to C is 6.79 miles
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Step-by-step explanation:
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Substitute values and solve for <em>b</em>. Then, you obtain: