Solve the triangle with the law of sines

see below

Step-by-step explanation:

We can use the law of sines

sin 80             sin B

=

31                       14

Using cross products

14 sin 80 = 31 sin B

14/31  sin 80 = sin B

.984807753 = sin B

Taking the inverse sin of each side

sin ^ -1 ( .444751888) =  B

26.41 = B

The sum of the angles of a triangle is 180

A+B+C = 180

80 + 26.41 + C =180

106.41 + C = 180

C = 73.59

We can use the law of sines to find c

sin 80             sin 73.59

=

31                       c

c sin 80 = 31 sin 73.59

c =  31 sin 73.59 / sin 80

c = 30.20

AB = 30.20

ion

step-by-step explanation:

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x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)