Question

the vertices of the Tri angle are (1,4,2) B(-2,1,2)C(2,3,-4) find the angle of a,b,c​

Answer 1

QUESTION

the vertices of the Tri angle are (1,4,2) B(-2,1,2)C(2,3,-4) find the angle of a,b,c​

A = 90°,  B ≈ 55.46° and C ≈ 34.54°

The vectors along the sides are:

AB = B - A = ( -3, -3, 0 ),  BC = C - B = ( 4, 2, -6 ),  CA = A - C = ( -1, 1, 6 ).

The squares of the lengths of the sides are then

|AB|² = 9 + 9 + 0 = 18

|BC|² = 16 + 4 + 36 = 56

|CA|² = 1 + 1 + 36 = 38

Notice that |AB|² + |CA|² = |BC|², so by the converse of Pythagoras' Theorem, there is a right angle at A.

For the angle at B, we have

cos B = |AB| / |BC| = 3√2 / 2√14 = 3 / 2√7

 $=> B ≈ 55.46°and C = 90° - B ≈ 34.54°$

HENCE THE ANSWER IS

=> B ≈ 55.46°

and C = 90° - B ≈ 34.54°