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Andreas93
3 months ago
9

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.

Mathematics
1 answer:
PIT_PIT [12.4K]3 months ago
8 0

Answer:

6.79 miles

Step-by-step explanation:

Consider triangle ABC where A marks the starting point and C indicates the end point.

|AB|=5.2 miles

|BC|=3.0 miles

∠ABC = 90 + 75 = 165°

We're given two side lengths and an angle that is not opposite to either side.

The approach to resolve this scenario is known as the Cosine Rule.

Each side opposite an angle is designated by the corresponding lowercase letter.

The Cosine Rule asserts that:

b² = a² + c² - 2acCosB

|AC|²=3² + 5.2² - (2 × 5.2 × Cos 165°)

|AC|²=9 + 27.04 + 10.05

|AC|²=46.09

|AC|=√46.09=6.79 miles

Thus, the straight-line distance from A to C measures 6.79 miles

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