Question

In triangle ABC, mA=35, mB=40, and a=9. Which equation should you solve for b?

A. sin35/b=sin40/9
B. sin35/9=sin40/b
C. cos35/9=cos40/b
D.b sqaure=9 square-2(9)bcos40

Answer 1

B.
`(sin 35)/(9)=(sin 40 )/(b)`

Explanation:

We are given that in a triangle ABC.
`m\angle =35^(\circ)`

`m\angle B=40^(\circ)`

a=9

We have to find an equation which solve for b

We know that a sine law

`(a)/(sine A)=(b)/(sinB)=(c)/(sinC)`

Using above formula of sine law

Substituting all given values in the above formula of sine law

Then we get

`(9)/(sin 35)=(b)/(sin 40)`

By cross multiply then we get

`sin 40* 9=sin35 * b`

`(sin 40 * 9)/(b)= sin 35`

Using division property of equality

`( sin 40)/(b)=(sin 35)/(9)`

Using division property of equality

Hence, option B is true option for solving b.

Answer:B.
`(sin 35)/(9)=(sin 40 )/(b)`

Answer 2

B. sin35/9=sin40/b

Explanation:

The law of sines tells you ...

sin(A)/a = sin(B)/b

Filling in the given values, you get ...

sin(35°)/9 = sin(40°)/b