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denis23
1 month ago
7

1. The cities of Dallas, Charleston, and Indianapolis form a triangle. The distance from Dallas to

Mathematics
1 answer:
PIT_PIT [12.4K]1 month ago
4 0

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.

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