Area of a triangle

Nov 2009
468
14
Triangle ABC
AC=5
BC=8
Angle ACB=75 degrees

Not sure how to do this, can't apply base height formula, nor pythagoras' theorem, nor heron's formula. What do i do?
 
Dec 2007
3,184
558
Ottawa, Canada
Calculate AB using Law of Cosines. Then call on Mr. Heron.
 
Nov 2009
468
14
what is the law of cosines?

Is there a law of sines/tans?
 

e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
Triangle ABC
AC=5
BC=8
Angle ACB=75 degrees

Not sure how to do this, can't apply base height formula, nor pythagoras' theorem, nor heron's formula. What do i do?
Use the formula for the area of a triangle (which is derived from the base, height formula)

\(\displaystyle A = \frac{1}{2}ab \sin C\)

Where

  • a = BC
  • b = AC
  • C = Angle ABC

This is because by convention:
side a is opposite angle A
side b is opposite angle B
side c is opposite angle C