Question

In a ΔABC, if `("b" + "c")/11 = ("c" + "a")/12 = ("a" + "b")/13`, then cos C = ______.

पर्याय

• `7/5`

• `5/7`

• `17/16`

• `("a"sin  (5pi)/8)/(1/sqrt(2))`

Answer 1

In a ΔABC, if `("b" + "c")/11 = ("c" + "a")/12 = ("a" + "b")/13`, then cos C = `5/7`.

Explanation:

Let `sqrt(2)`

∴ b + c = 11k   ......(i)

c + a = 12k  ......(ii)

and a + b = 13k  ......(iii)

From (i) + (ii) + (iii), 2(a + b + c) = 36k

∴ a + b + c = 18k   ......(iv)

Now, (iv) – (i) gives, a= 7k

(iv) – (ii) gives, b = 6k

(iv) – (iii) gives, c = 5k

Now, cos C = `("a"^2 + "b"^2 - "c"^2)/(2"ab")`

= `((7"k")^2 + (6"k")^2 - (5"k")^2)/(2 xx (7"k") xx (6"k"))`

= `(49"k"^2 + 36"k"^2 - 25"k"^2)/(84"k"^2)`

= `(60"k"^2)/(84"k"^2)`

= `5/7`