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Which equation is true for triangle QRS?

Which equation is true for triangle QRS?-example-1

2 Answers

6 votes

Answer:

(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.

User Shannette
by
7.7k points
5 votes

Answer:

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)

User Arelys
by
8.7k points

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