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

hey! so 1 (25) out of 4 (100) is 25 so your answer is 25%. it's like quarters!

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.