Ashok Shah

The Area of Triangle

The area of triangle ABC with the given measurement as shown in fig is '∆'. 's' is the semi-perimeter of the triangle such that 2s=().We know, area of triangle is given by;From Half-angle formula, ...

The Tangent Law

From Sine Law,         →b = 2R sin B............(i)    →c = 2R sin C............(ii)Subtracting eqn (ii) from (i)            b - c = 2R(sin B - sin C)............(I)Adding eqn (i) and (ii)     b + ...

The Half-angle Formula

For Cosine values,The other results of cosine values in Half-angle formula follow the same process.For Sine valuesThe other results of sine value in Half-angle formula follow the same process.For T...

The Projection Law

From the Sine Law, We have,  b =2R sin B...........(i)  c =2R sin C...........(ii) =2R sin A...........(iii)To Prove: i) b cos C + c cos B = Taking LHS;= b cos C + c cos B= 2R sin B. cos C + 2R cos...

The Sine Law in terms of Circum-Radius

Let ABC be the triangle with all three vertex on the circumference of the circle with center O as shown in fig above.BO is drawn if the angle is either acute or obtuse as shown in fig(i) and fig(ii...

The Sine Law

Let ABC be a triangle, acute angled in fig(i), obtuse angled in fig(ii) and right angled in fig(iii).A perpendicular AD is drawn on BC [BC is produced to D in fig. (ii) and D coincides C in fig (ii...

The Cosine Law - Proof

Let ABC be a triangle, acute angled in fig. (i), obtuse angled in fig. (ii) and right angled in fig (iii) .BD is drawn perpendicular to AC from point B in fig(i) and fig(ii).To prove:  Proof:1. Whe...

Properties of Triangle - Formula

Introduction:A triangle consists of three side and three angles which is collectively known as the six elements. In a triangle ABC, the side opposite to ∠A is denoted by '', the side opposite to ...