Question

Which equation is true for triangle QRS?

Answer 1

(A)

Explanation:

Using the law of sines,
`(sinA)/(a)=(sinB)/(b)=(sinC)/(c)`

From the given figure, we have RQ=2.4, QS=3.5 and RS is unknown.

In order to use the law of sines, side should be opposite to the angle being considered, therefore

`(sin100^(\circ))/(3.5)=(sinS)/(2.4)` holds.

For,
`(sin100)/(3.5)=(sinQ)/(2.4)`, this does not holds because, the side opposite to angle Q is RS which is unknown, thus this option is incorrect.

For,
`(sin100)/(2.4)=(sinS)/(3.5)`, does npot holds, because the side opposite to angle R is of measure 3.5 and not 2.4, thus, this option is incorrect.

For,
`(sin100)/(2.4)=(sinQ)/(3.5)`, does npot holds, because the side opposite to angle R is of measure 3.5 and not 2.4 and the side opposite to angle Q is RS,thus this option is incorrect.

Answer 2

The first option
`(sin 100\°)/(3.5)=(sin S\°)/(2.4)`

Explanation:

we know that

In the triangle QRS

Applying the law of sines

`(sin Q\°)/(RS)=(sin R\°)/(QS)=(sin S\°)/(QR)`

in this problem we have

`QR=2.4\ units\\ QS=3.5\ units\\R=100\°`

substitute in the formula above

`(sin Q\°)/(RS)=(sin 100\°)/(3.5)=(sin S\°)/(2.4)`

therefore

The equation that is true for the triangle QRS is

`(sin 100\°)/(3.5)=(sin S\°)/(2.4)`