Adanzaannalizaidn
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ΔPRQ is a 30°-60°-90° triangle.
1. If PQ=8,find RQ and PR. ​

Sagot :

Answer:

1.

Given: PRQ is a 30-60-90 triangle

           PQ= 8

In a 30-60-90 triangle, the side across from the 60 degrees equals [tex]\frac{\sqrt{3} }{2}[/tex] times the side across from the hypotenuse. Therefore,

      [tex]QR=\frac{\sqrt{3} }{2} PQ[/tex]     ⇒   [tex]QR=(\frac{\sqrt{3} }{2}) (8)[/tex]

        Multiply fractions:    [tex](a) \frac{b}{c} = \frac{(a)(b)}{c}[/tex]  ⇒  [tex]\frac{(8)(\sqrt{3}) }{2}[/tex]

        Then divide   [tex]\frac{8}{2} = 4[/tex]

Hence,  RQ =  [tex]4\sqrt{3}[/tex]

2. PR=?

In a 30-60-90 triangle, the hypotenuse equals twice the side across from the 30 degrees. Hence, PQ=2PR

    Since PQ=8, therefore

   2PR   =    8      Cancel out 2 then divide 8 by 2 to get 4. Hence,

     2           2

PR = 4