Half-Angle Formula and the Area of a Triangle
Half-Angle Formula and the Area of a Triangle: Overview
This topic covers concepts such as Trigonometric Ratios of Half Angles of a Triangle, Area of Triangle, General Formula for Area of Triangle, Heron's Formula for Area of Triangle, and Napier's Analogy—Tangent Rule.
Important Questions on Half-Angle Formula and the Area of a Triangle
If is the perpendicular distance from on of a triangle , prove that .

If the sides of a triangle are in A.P., then show that cot are also in A.P.

[x] .

[ix].

In a ; prove that, .

In a right-angled triangle , right angled at , let be the incentre, If units and units, find the area of .

If and be the lengths of the perpendiculars from circum centre of a triangle on the sides and respectively, then show that
.

Let be a triangle such that and . Choose points on respectively, such that . Then is

If in a , two sides are , and , then

If in a , two sides are , and . Then, find the value of if length of the side is

If in a , two sides are , and . Find .

If is right-angled at . Prove that : .

In a , the tangent of half the difference of two angles is one-third the tangent of half the sum of the angles. Determine the ratio of the sides opposite to the angles.

Show that in , .

Show that in .

With the usual notations prove that area of .

If in , , then prove that are in

Show that for , where is the area of triangle.

In , if and , then find the value of .

In , if and , then find the value of .
