erikaasencio11 erikaasencio11
  • 12-06-2019
  • Mathematics
contestada

what is the measurement of angle p? Round your answer to the nearest degree.


A. 29°

B.42°

C.65°

D.78°

what is the measurement of angle p Round your answer to the nearest degree A 29B42C65D78 class=

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Аноним Аноним
  • 12-06-2019

You can use the law sines, which states that in a triangle the ratio between one side length and the sine of the opposite angle is constant.

So, we have

[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}=\dfrac{PQ}{\sin(R)}[/tex]

In particular, we can use

[tex]\dfrac{PR}{\sin(Q)}=\dfrac{QR}{\sin(P)}[/tex]

to write

[tex]\dfrac{68}{\sin(73)}=\dfrac{47.6}{\sin(P)} \iff \sin(P) = \dfrac{47.6\sin(73)}{68}\approx 0.66[/tex]

Which means

[tex]P\approx \arcsin(0.66)\approx 42[/tex]

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