Question

In triangle abc, if A=120 degrees, a=8 and b=3, then angle B=

Answer 1

The angle of B is
`\angle B=19^(\circ)`

Step-by-step explanation:

It is given that
`\angle A=120^(\circ)` and
`a=8, b=3`

To determine the
`\angle B`, let us use the law of sine formula.

Thus, we have,

`(Sin A)/(a) =(Sin B)/(b)`

Substituting the values in the formula, we have,

`(Sin 120)/(8) =(Sin B)/(3)`

Multiplying both sides by 3,we get,

`(3(0.866))/(8) ={Sin B}`

Simplifying and dividing, we get,

`0.32475=Sin B`

Multiplying both sides by
`\sin ^(-1)`, we get,

`\sin ^(-1)(0.32475)=B`

Thus,
`B=18.95^(\circ)=19^(\circ)`

Hence, The angle of B is
`\angle B=19^(\circ)`