Find, correct to the nearest degree, the three angles of the triangle with the g

Yulia 2021-10-28 Answered
Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
A(1,0,-1), B(5,-3,0), C(1,5,2)
Find CAB,ABC,BCA
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Expert Answer

sovienesY
Answered 2021-10-29 Author has 89 answers
AB=(5,3,0)(1,0,1)=(4,3,1)
AC=(1,5,2)(1,0,1)=(0,5,3)
|AB|=42+32+12=26
|AC|=0+52+32=34
Use:
ABAC=|AB||AC|cosCAB
(4,3,1)(0,5,3)=2634cosCAB
4035+13=2634cosCAB
12=2634cosCAB
cosCAB=0.404
CAB=113.8 degree
BA=(1,0,1)(5,3,0)=(4,3,1)
BC=(1,5,2)(5,3,0)=(4,8,2)
|BA|=26
|BC|=42+82+22=84
Use:
BABC=|BA||BC|cosABC
(4,3,1)(4,8,2)=2684cosABC
16+242=2684cosABC
cosABC=0.813
ABC=35.6 degree
Sum of all angle = 180
BCA+35.6+113.8=180
BCA=30.6 degree
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