Question

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP(25 points)

Answer 1

Answer: I hope it helps :)

• x=6 , y=6√3
• x =23√3 , y=23
• u =12 , v= 6
• a =18√2 , b =18
• x = 13 , y= 13

Explanation:

1.

`Hypotenuse =x\\Opposite =y \\Adjacent =6\\\alpha = 6\\Let's\: find\: the \:hypotenuse\: first\\Using SOHCAHTOA\\Cos \alpha = (adj)/(hyp) \\Cos 60 = (6)/(x) \\(1)/(2) =(6)/(x) \\Cross\:Multiply\\x = 12\\Let's\: find\: y\\Hyp^2=opp^2+adj^2\\12^2=y^2+6^2\\144=y^2+36\\144-36=y^2\\108=y^2\\√(108) =√(y^2) \\y=6√(3)`

2.

`Opposite =x\\Hypotenuse = 46\\Adjacent =y \\\alpha =60\\Using \: SOHCAHTOA\\Sin \alpha =(opp)/(adj) \\Sin 60=(x)/(46)\\\\(√(3) )/(2) =(x)/(46) \\2x=46√(3) \\x = (46√(3) )/(2) \\x =23√(3) \\\\Hyp^2=opp^2+adj^2\\46^2=(23√(3) )^2+y^2\\2116=1587+y^2\\2116-1587=y^2\\529=y^2\\√(529) =√(y^2) \\y = 23`

3.

`Hypotenuse = u\\Opposite =6√(3) \\Adjacent = v\\\alpha =60\\Sin\: 60 = (6√(3) )/(u) \\(√(3) )/(2) =(6√(3) )/(u) \\12√(3) =u√(3) \\\\(12√(3) )/(√(3) ) =(u√(3) )/(√(3) ) \\u = 12\\Hyp^2=opp^2+adj^2\\12^2= (6√(3) )^2+v^2\\144=108+v^2\\144-108=v^2\\36 = v^2\\√(36) =√(v^2) \\\\v =6`

4.

`Hypotenuse = a\\Opposite =18 \\Adjacent = b\\\alpha =45\\Tan \alpha = opp/adj\\Tan \:45 =18/b\\1=(18)/(b)\\ b = 18\\\\Hyp^2=Opp^2+Adj^2\\a^2 = 18^2+18^2\\a^2=324+324\\a^2=648\\√(hyp^2) =√(648)\\ \\a =18√(2)`

5.

`Hypotenuse = 13√(2)\\ Opposite =x\\Adjacent = y\\\alpha =45\\Sin\:\alpha = opp/hyp\\Sin 45=x/13√(2)\\ \\(√(2) )/(2) =(x)/(13√(2) ) \\2x=26\\2x/2=26/2\\\\x = 13\\\\Hyp^2=opp^2+adj^2\\(13√(2))^2=13^2+y^2\\ 338=169+y^2\\338-169=y^2\\169=y^2\\√(169) =√(y^2) \\13 = y`