How do you find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (3,3) and C = (3, -2)?

1 Answer
Nov 23, 2016

Please see the explanation.

Explanation:

It will not change anything with regard to side lengths or angles, if we add 1 to all of the x coordinates:

A=(0,0),B=(4,3),andC=(4,2)

The length of side "a" (from C to B), is easy, because B and C have the same x coordinate, therefore, you just use the y coordinate difference:

a=(32)
a=5

The length of side "b" (from A to C) is made easier by A being the origin:

b=42+(2)2=20

The same is true for the length of side "c" (from A to B):

c=42+32=5

It is an isosceles triangle so we need to find B and we know that A=C

Use the Law of Cosines:

b2=a2+c22(a)(c)cos(B)

20=25+2550cos(B)

2050=1cos(B)

cos(B)=35

B=cos1(35)53

A=C=180532=63.5