Respuesta :

calculista

Answer:

The first option [tex]\frac{sin 100\°}{3.5}=\frac{sin S\°}{2.4}[/tex]

Step-by-step explanation:

we know that

In the triangle QRS

Applying the law of sines

[tex]\frac{sin Q\°}{RS}=\frac{sin R\°}{QS}=\frac{sin S\°}{QR}[/tex]

in this problem we have

[tex]QR=2.4\ units\\ QS=3.5\ units\\R=100\°[/tex]

substitute in the formula above

[tex]\frac{sin Q\°}{RS}=\frac{sin 100\°}{3.5}=\frac{sin S\°}{2.4}[/tex]

therefore

The equation that is true for the triangle QRS is

[tex]\frac{sin 100\°}{3.5}=\frac{sin S\°}{2.4}[/tex]

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Answer:

(A)

Step-by-step explanation:

Using the law of sines, [tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

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

[tex]\frac{sin100^{\circ}}{3.5}=\frac{sinS}{2.4}[/tex] holds.

For, [tex]\frac{sin100}{3.5}=\frac{sinQ}{2.4}[/tex], this does not holds because, the side opposite to angle Q is RS which is unknown, thus this option is incorrect.

For, [tex]\frac{sin100}{2.4}=\frac{sinS}{3.5}[/tex], 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, [tex]\frac{sin100}{2.4}=\frac{sinQ}{3.5}[/tex], 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.

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