A trig formula for area of a triangle

1、A Trig Formula for the Area of a Triangle,In a right angled triangle, the 3 trig ratios for an angle x are defined as follows:,opposite,hypotenuse,In a right angled triangle, the 3 trig ratios for an angle x are defined as follows:,hypotenuse,adjacent,In a right angled triangle, the 3 trig ratios fo

2、r an angle x are defined as follows:,opposite,adjacent,Using the trig ratios we can find unknown angles and sides of a right angled triangle, provided that, as well as the right angle, we know the following:,either 1 side and 1 angle,or 2 sides,(3 s.f.),We will now find a formula for the area of a t

3、riangle that is not right angled, using 2 sides and 1 angle.,a, b and c are the sides opposite angles A, B and C respectively. ( This is a conventional way of labelling a triangle ).,ABC is a non-right angled triangle.,b,a,c,Draw the perpendicular, h, from C to BA.,h,ABC is a non-right angled triang

4、le.,Draw the perpendicular, h, from C to BA.,h,- - - - - (1),In,ABC is a non-right angled triangle.,Draw the perpendicular, h, from C to BA.,h,- - - - - (1),In,ABC is a non-right angled triangle.,- - - - - (1),In,Draw the perpendicular, h, from C to BA.,ABC is a non-right angled triangle.,Substituti

5、ng for h in (1),A,- - - - - (1),In,Draw the perpendicular, h, from C to BA.,ABC is a non-right angled triangle.,c,b,a,a,C,B,A,Substituting for h in (1),- - - - - (1),In,Draw the perpendicular, h, from C to BA.,ABC is a non-right angled triangle.,Any side can be used as the base, so,The formula alway

6、s uses 2 sides and the angle formed by those sides,Any side can be used as the base, so,The formula always uses 2 sides and the angle formed by those sides,Any side can be used as the base, so,The formula always uses 2 sides and the angle formed by those sides,Any side can be used as the base, so,Th

7、e formula always uses 2 sides and the angle formed by those sides,1.Find the area of the triangle PQR.,Solution: We must use the angle formed by the 2 sides with the given lengths.,1.Find the area of the triangle PQR.,Solution: We must use the angle formed by the 2 sides with the given lengths.,We k

8、now PQ and RQ so use angle Q,1.Find the area of the triangle PQR.,Solution: We must use the angle formed by the 2 sides with the given lengths.,We know PQ and RQ so use angle Q,cm2 (3 s.f.),A useful application of this formula occurs when we have a triangle formed by 2 radii and a chord of a circle.,r,B,A,r,The area of triangle ABC is given by,The area of a triangle formed by 2 radii of length r of a circle and the chord joining them is given by,where is the angle between t