Answer:
30. [tex]x=5\\y=5\sqrt{3}[/tex]
31. [tex]x=4\\y=4\sqrt{3}[/tex]
32. [tex]x=6\\y=6\sqrt{3}[/tex]
33. [tex]x=4.5\\y=\frac{9\sqrt{3} }{2}[/tex]
34. [tex]x=40\\y=40\sqrt{3}[/tex]
35. [tex]x=7.5\\y=\frac{15\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Use SOHCAHTOA to find one of the missing sides, then use the pythagorean theorem ([tex]x^{2}+ y^{2} =z^{2}[/tex]) to find the other one
[tex]sin=\frac{opposite}{hypotenuse}[/tex]
[tex]cos=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan=\frac{opposite}{adjacent}[/tex]
30.
First find [tex]x[/tex] using Sin
[tex]sin(30)=\frac{x}{10}[/tex]
[tex]10*sin(30)=x[/tex]
[tex]x=5[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]5^{2}+ y^{2} =10^{2}[/tex]
[tex]25+y^{2} =100[/tex]
[tex]y^{2} =75[/tex]
[tex]\sqrt{y^{2}} =\sqrt{75}[/tex]
[tex]y=5\sqrt{3}[/tex]
32.
First use Sin to find [tex]x[/tex]
[tex]sin(30)=\frac{x}{8}[/tex]
[tex]8*sin(30)=x[/tex]
[tex]x=4[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]4^{2}+ y^{2} =8^{2}[/tex]
[tex]16+y^{2} =64[/tex]
[tex]y^{2} =48[/tex]
[tex]\sqrt{y^{2} } =\sqrt{48}[/tex]
[tex]y=4\sqrt{3}[/tex]
32.
First use Sin to find [tex]x[/tex]
[tex]sin(30)=\frac{x}{12}[/tex]
[tex]12*sin(30)=x[/tex]
[tex]x=6[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]6^{2}+ y^{2} =12^{2}[/tex]
[tex]36+y^{2} =144[/tex]
[tex]y^{2} =108[/tex]
[tex]\sqrt{y^{2} } =\sqrt{108}[/tex]
[tex]y=6\sqrt{3}[/tex]
33.
First use Sin to find [tex]x[/tex]
[tex]sin(30)=\frac{x}{9}[/tex]
[tex]9*sin(30)=x[/tex]
[tex]x=4.5[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]4.5^{2}+ y^{2} =9^{2}[/tex]
[tex]20.25+y^{2} =81[/tex]
[tex]y^{2} =60.75[/tex]
[tex]\sqrt{y^{2} } =\sqrt{60.75}[/tex]
[tex]y=\frac{9\sqrt{3} }{2}[/tex]
34.
First use Sin to find [tex]x[/tex]
[tex]sin(30)=\frac{x}{80}[/tex]
[tex]80*sin(30)=x[/tex]
[tex]x=40[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]40^{2}+ y^{2} =80^{2}[/tex]
[tex]1600+y^{2} =6400[/tex]
[tex]y^{2} =4800[/tex]
[tex]\sqrt{y^{2} } =\sqrt{4800}[/tex]
[tex]y=40\sqrt{3}[/tex]
35.
First use Sin to find [tex]x[/tex]
[tex]sin(30)=\frac{x}{15}[/tex]
[tex]15*sin(30)=x[/tex]
[tex]x=7.5[/tex]
Then use the pythagorean theorem to find [tex]y[/tex]
[tex]7.5^{2}+ y^{2} =15^{2}[/tex]
[tex]56.25+y^{2} =225[/tex]
[tex]y^{2} =168.75[/tex]
[tex]\sqrt{y^{2} }=\sqrt{168.75}[/tex]
[tex]y=\frac{15\sqrt{3} }{2}[/tex]
