Given: circle o, r=a, ab = b, ac = c
(1) find m∠bac
(2) find m∠bac if b=2, c=4, a=3

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)

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step-by-step explanation: