Question

Determine mzB if a = 14, b = 15.0 = 17 of AABC. Determine theangle to the nearest tenth of a degree.(Here A is the angle opposite side a. B is the angle opposite side b, etc.)

Answer 1

Given:

a=14

b=15

c=17

Find measure of angle B.

Applying law of cosines, we have:

`b^2=a^2+c^2-2ac\cos (B)`

Putting the values,we have:

`15^2=14^2+17^2-2*14*17*\cos (B)`

We have to find B so ,

`\cos \text{ (B)=}(196+289-225)/(476)`
`\begin{gathered} \cos (B)=(260)/(476) \\ =0.5462 \end{gathered}`
`B=\cos ^(-1)\text{ 0.5462}`

Hence, the angle B is nearly 60 degrees.

That is,

`m\angle B=60^(\circ)`

This is required answer.