You can find x by using the pythagorean theorem:
Bring everything to the same side:
The solutions to this equation are and 1. We can't accept the negative solutions because it would lead to negative lengths, so we have
This implies that the triangle is a 3-4-5 triangle. Now, you can use the law of sines to state
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:
where A = angle A = <A
Given that
b = 5.2 miles
c = 2.0 miles
<A = 115° (from the diagram)
Hence,
The straight-line distance between the starting point and the end of the race is 6.31 mi
