ABC is a triangle in which AB=6 cm, BC =8 cm and CA=10 cm. What is the value of cot(A/4)?

Explanation

First , we will find the area of the given triangle using Heron`'`s rule.

Here, `S = (a+b+c)/2 = (6+8+10)/2 = 12`

`:. Area(Ar) = sqrt(12(12-6)(12-8)(12-10)) = sqrt(12**6**4**2) = 24cm^2`

`:. tan(A/2) = (Ar)/(s(s-a)) = 24/(12**(12-8)) = 1/2`

We know, `tan2X = (2tanX)/(1-tan^2X)`

`(2tan(A/4))/(1-tan^2(A/4)) = 1/2`

`=>tan^2(A/4) +4tan(A/4) - 1 = 0`

`=>tan (A/4) = (-4+-sqrt(16+4))/2 = -2+-sqrt5`

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