Question

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 2.0 mi to the finish line.
In miles, what is the straight-line distance from the starting point to the end of the race?

Answer 1

Answer:

6.31 mi

Step-by-step explanation:

The diagram below explains the solution better.

From the diagram,

C = starting point of the race.

A = end of the first part of the race.

B = end of the race.

Using Cosine rule, we can find the straight-line distance between the starting point and the end of the race.

Cosine rule states that:

$a^2 = b^2 + c^2 - 2bc[cos(A)]$

where A = angle A = <A

Given that

b = 5.2 miles

c = 2.0 miles

<A = 115° (from the diagram)

Hence,

$a^2 = 5.2^2 + 2.0^2 - 2*5.2*2.0[cos(115)]\\\\a^2 = 27.04 + 4 - 20.8[cos(115)]\\\\a^2 = 31.04 + 8.79\\\\a^2 = 39.83\\\\a = \sqrt{39.83}\\ \\a = 6.31 mi$

The straight-line distance between the starting point and the end of the race is 6.31 mi