Question

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

Charleston is 980 mies, Charleston to Indianapolis is 595 mies, and Indianapolis to Dallas is 764

mies. If Dallas and Charleston lie on the same latitude, find the bearing from Charleston to

Indianapolis.

Answer 1

Answer: 130 degree

Step-by-step explanation:

Given that

The distance from

Dallas to Charleston = 980 miles Charleston to Indianapolis = 595 miles,

Indianapolis to Dallas is 764 mies.

If Dallas and Charleston lie on the same latitude, find the bearing from Charleston to Indianapolis.

Let us use cosine formula 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

Let us also calculate the angle at Indianapolis by using sine rule

980/sinI = 764/sin 51.2

Reciprocal both sides

SinI/980 = sin 51.2/764

Sin I = 980 × sin52.1/764

Sin I = 0.9996

I = 88.5 degree

The bearing = 270 - ( 51.2 + 88.5)

= 270 - 140

= 130 degree.

Answer 2

In this exercise we have to use the knowledge of triangles to calculate the angle of this geometric figure, in this way we can say that:

130 degree

Given that the distance from dallas to Charleston and Charleston to Indianapolis and Indianapolis to Dallas, we can use the the cosine formula to find the angle at Charleston, so we have:

$764^2 = 980^2+595^2-2(980)(595)cos\phi\\583696 = 1314425-1166200cos\phi\\-1166200cos\phi = -730729\\Cos\phi = 0.6266\\\phi = 51.2$

Let us also calculate the angle at Indianapolis by using sine rule:

$980/sin\theta = 764/sin (51.2)\\Sin\theta/980 = sin 51.2/764\\Sin\theta = 980 * sin52.1/764\\Sin \theta = 0.9996\\\theta = 88.5 degree = 270 - ( 51.2 + 88.5)\\= 270 - 140\\= 130 degree.$

See more about triangles at brainly.com/question/2269348