SOLUTION: A vertices of a triangle A(1,2) B(4,5) C(3,-2). (a) find the surd form the length AB, BC and AC (b) show that cosA=-1/(square root of 10) and deduce the value of sinA in surd for

Algebra ->  Equations -> SOLUTION: A vertices of a triangle A(1,2) B(4,5) C(3,-2). (a) find the surd form the length AB, BC and AC (b) show that cosA=-1/(square root of 10) and deduce the value of sinA in surd for      Log On


   

Question 1137926: A vertices of a triangle A(1,2) B(4,5) C(3,-2).
(a) find the surd form the length AB, BC and AC
(b) show that cosA=-1/(square root of 10) and deduce the value of sinA in surd form
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
A vertices of a triangle A(1,2) B(4,5) C(3,-2).

(a) find the surd form the length AB, BC and AC

A(1,2) B(4,5)
AB=sqrt%28%284-1%29%5E2%2B%285-2%29%5E2%29
AB=sqrt%283%5E2%2B3%5E2%29
AB=sqrt%282%2A3%5E2%29
AB=sqrt%2818%29
AB=3sqrt%282%29

B(4,5) C(3,-2)
BC=sqrt%28%283-4%29%5E2%2B%28-2-5%29%5E2%29
BC=sqrt%28%28-1%29%5E2%2B%28-7%29%5E2%29
BC=sqrt%281%2B49%29
BC=sqrt%2850%29
BC=5sqrt%282%29

A(1,2) C(3,-2)
AC=sqrt%28%283-1%29%5E2%2B%28-2-2%29%5E2%29
AC=sqrt%282%5E2%2B%28-4%29%5E2%29
AC=sqrt%284%2B16%29
AC=sqrt%2820%29

AC=2sqrt%285%29

(b) show that+cos%28A%29=-1%2Fsqrt%2810%29 and deduce the value of sin%28A%29 in surd form
cos%28A%29+=++%28b%5E2+%2B+c%5E2-+a%5E2%29%2F%282bc%29
use
AB=c=sqrt%2818%29
BC=a=sqrt%2850%29
AC=b=sqrt%2820%29 ..will be easier


cos%28A%29+=++%2820+%2B+18-50%29%2F%2812sqrt%2810%29%29
cos%28A%29+=++%28-12%29%2F%2812sqrt%2810%29%29
cos%28A%29+=++%28-cross%2812%291%29%2F%28cross%2812%29sqrt%2810%29%29
cos%28A%29+=++-1%2Fsqrt%2810%29
sin%28A%29=..........since sin%5E2%28A%29=1-cos%5E2%28A%29+=1-%281%2Fsqrt%2810%29%29%5E2=1-1%2F10=9%2F10=>
sin%28A%29=sqrt%289%2F10%29
sin%28A%29=sqrt%289%29%2Fsqrt%2810%29
sin%28A%29=3%2Fsqrt%2810%29
sin%28A%29=3sqrt%2810%29%2F10