Area of Triangle
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AREA OF A TRIANGLE
If D represents the area of a triangle then
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D = 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B |
D = {s(s-a)(s-b)(s-c)}1/2
D = abc/4R
D = rs
where 2s= a+b+c and r is the inradius of the triangle
NOTE:
RELATION BETWEEN r AND R
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r = 4 R sin A/2 sin B/2 sin C/2 |
TRIGONOMETRIC RATIOS OF HALF ANGLES IN TERMS OF THE SIDES
- Sin A/2 = {(s-b)(s-c)/bc}1/2
- Cos A/2 = {s(s-a)/bc}1/2
- Tan A/2 = {(s-b)(s-c)/s(s-a)}1/2
- Sin B/2 = {(s-c)(s-a)/ca}1/2
- Cos B/2 = {s(s-b)/ac}1/2
- Tan B/2 = {(s-c)(s-a)/s(s-b)}1/2
- Sin C/2 = {(s-a)(s-b)/ab}1/2
- Cos C/2 = {s(s-c)/ab}1/2
- Tan C/2 = {(s-c)(s-a)/s(s-c)}1/2