Find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (2,1), C = (1,-2).

opositor5t 2022-08-08 Answered
Find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (2,1), C = (1,-2).
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Answers (1)

Deja Navarro
Answered 2022-08-09 Author has 17 answers
A B ¯ = ( 1 2 ) 2 + ( 0 1 ) 2 = 9 + 1 = 10
B C ¯ = ( 1 2 ) 2 + ( 2 1 ) 2 = 1 + 9 = 10
A C ¯ = ( 1 1 ) 2 + ( 0 + 2 ) 2 = 4 + 4 = 2 2
we will use
a 2 = b 2 + c 2 2 b c cos ( θ ) where θ is angle A
we have:
cos ( A B C ) = A B 2 ¯ + B C 2 ¯ A C 2 ¯ 2 B C 2 ¯ A B 2 ¯ = 10 + 10 8 2 10 10 = 12 20 = 3 5
A B C = cos 1 ( 3 5 ) = 53.13 0
cos ( A C B ) = ( B C ) 2 + ( A C ) 2 ( A B ) 2 2 B C A C = 10 + 8 10 2 10 8 = 8 2 80 = 4 4 5 = 5 5
B A C = 63.43 0
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