1. cos⁻¹(b/2a)-cos⁻¹(c/2a)
2.cos⁻¹(1/3)-cos⁻¹(2/3)
Step-by-step explanation:
Given:
r = a
AB = b
AC = c
To find : ∠BAC
Construction:
Join OA ,OB and OC.
Solution:
Now we have two triangles : ΔOAB and ΔOAC after construction.
We can find ∠OAB and ∠OAC by applying cosine formula for ΔOAB and ΔOAC.
∠BAC = ∠OAB - ∠OAC
Applying cosine formula for ΔOAB,
cos∠OAB =
∠OAB = cos⁻¹(b/2a)
Applying cosine formula for ΔOAC,
cos∠OAC =
∠OAC = cos⁻¹(c/2a)
Now
∠BAC = ∠OAB - ∠OAC
= cos⁻¹(b/2a) - cos⁻¹(c/2a)
If a=3 b=2 c=4, we get
∠BAC = cos⁻¹(1/3) - cos⁻¹(2/3)