A 30 60 90 Triangle with a long leg of 12 Find the length of the hypotenuse and the short leg.

Step-by-step explanation:   5 17 7 22

the long leg would be opposite the middle angle 60°,  the hypotenuse is opposite the 90° angle thus leaving the 30° is opposite the short leg

1) use sin Θ = opp / hyp       sin 60° = 12 / hyp    to find the hypotenuse

1) use sin Θ = opp / hyp       sin 30° = opp/ hyp    to find the short leg

      hyp = 12 / sin(60)       = 13.856  hypotenuse

      opp = (12 / sin(60)) (sin 30)     =  6.92   short leg

short leg ²  + long leg ²  = hypotenuse ²

     48         +     144        =     192          sum of the legs squared = hyp²

7/2

(decimal: 3.5)

welcome ; )

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