Question

In ΔABC if a = 13, b = 14, c = 15, then find the value of `"cosec" A/2`.

Answer 1

s = `(a + b + c)/2`

= `(13 + 14 + 15)/2`

= 21

Using the half-angle formula: 

`sin  A/2 = sqrt(((s - b)(s - c))/(bc))`

`sin  A/2 = sqrt(((21- 14)(21 - 15))/((14)(15)))`

= `sqrt((7 xx 6)/(210))`

= `sqrt(42/210)`

= `sqrt(1/5)`

= `1/sqrt5`

`"cosec" A/2 = 1/(sin  A/2)`

= `1/(1/sqrt5)`

= `sqrt5`

= 2.236