contestada

In ARST, mZR = 92° and mZS = 71º. Which list has the sides of ARST in order from shortest to longest? O RS, ST, TR ORS, TR, ST O ST, RS, TR O TR, RS, ST O TR, ST, RS O ST, TR, RS

Respuesta :

From the sine law we have that:

[tex]\frac{\sin(17)}{SR}=\frac{\sin(71)}{RT}=\frac{\sin (92)}{ST}[/tex]

from the first part of the equality, we obtain:

[tex]\sin (17)RT=\sin (71)SR\Rightarrow SR=RT\frac{\sin (17)}{\sin (71)}[/tex]

since sin(17)/sin(71) is less that 1, we conclude that RT is longer than SR

Now, comparing SR and ST with the equalities, we have that:

[tex]\sin (17)ST=\sin (92)SR\Rightarrow SR=\frac{\sin (17)}{\sin (92)}ST[/tex]

Then ST is longer than SR, now we need to compare ST AND RT

[tex]\sin (71)ST=\sin (92)RT\Rightarrow RT=\frac{\sin (71)}{\sin (92)}ST[/tex]

Then ST is longer Than RT, we conclude that ST is longer than RT which is longer than SR then the correct option is the SECOND ONE (RS,TR,ST)

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