Answer: 130 degrees
Step-by-step explanation:
Given that
The distance from
Dallas to Charleston = 980 miles, from Charleston to Indianapolis = 595 miles, and from Indianapolis to Dallas is 764 miles.
Assuming that Dallas and Charleston are situated on the same latitude, we need to determine the bearing from Charleston to Indianapolis.
We will utilize the cosine rule to find the angle at Charleston.
764^2 = 980^2 + 595^2 - 2(980)(595)cosØ
583696 = 1314425 - 1166200cosØ
-1166200cosØ = -730729
CosØ = 0.6266
Ø = 51.2
Next, we calculate the angle at Indianapolis using the sine rule:
980/sinI = 764/sin 51.2
Reciprocate both sides:
SinI/980 = sin 51.2/764
Therefore, Sin I = 980 × sin 51.2/764
Sin I = 0.9996
I = 88.5 degrees
The bearing = 270 - (51.2 + 88.5)
= 270 - 140
= 130 degrees.
