Question

Can someone help me with this!!!!!

Answer 1

Answer:

30. $x=5\\y=5\sqrt{3}$

31.  $x=4\\y=4\sqrt{3}$

32. $x=6\\y=6\sqrt{3}$

33. $x=4.5\\y=\frac{9\sqrt{3} }{2}$

34. $x=40\\y=40\sqrt{3}$

35. $x=7.5\\y=\frac{15\sqrt{3} }{2}$

Step-by-step explanation:

Use SOHCAHTOA to find one of the missing sides, then use the pythagorean theorem ($x^{2}+ y^{2} =z^{2}$) to find the other one

$sin=\frac{opposite}{hypotenuse}$

$cos=\frac{adjacent}{hypotenuse}$

$tan=\frac{opposite}{adjacent}$

30.

First find $x$ using Sin

$sin(30)=\frac{x}{10}$

$10*sin(30)=x$

$x=5$

Then use the pythagorean theorem to find $y$

$5^{2}+ y^{2} =10^{2}$

$25+y^{2} =100$

$y^{2} =75$

$\sqrt{y^{2}} =\sqrt{75}$

$y=5\sqrt{3}$

32.

First use Sin to find $x$

$sin(30)=\frac{x}{8}$

$8*sin(30)=x$

$x=4$

Then use the pythagorean theorem to find $y$

$4^{2}+ y^{2} =8^{2}$

$16+y^{2} =64$

$y^{2} =48$

$\sqrt{y^{2} } =\sqrt{48}$

$y=4\sqrt{3}$

32.

First use Sin to find $x$

$sin(30)=\frac{x}{12}$

$12*sin(30)=x$

$x=6$

Then use the pythagorean theorem to find $y$

$6^{2}+ y^{2} =12^{2}$

$36+y^{2} =144$

$y^{2} =108$

$\sqrt{y^{2} } =\sqrt{108}$

$y=6\sqrt{3}$

33.

First use Sin to find $x$

$sin(30)=\frac{x}{9}$

$9*sin(30)=x$

$x=4.5$

Then use the pythagorean theorem to find $y$

$4.5^{2}+ y^{2} =9^{2}$

$20.25+y^{2} =81$

$y^{2} =60.75$

$\sqrt{y^{2} } =\sqrt{60.75}$

$y=\frac{9\sqrt{3} }{2}$

34.

First use Sin to find $x$

$sin(30)=\frac{x}{80}$

$80*sin(30)=x$

$x=40$

Then use the pythagorean theorem to find $y$

$40^{2}+ y^{2} =80^{2}$

$1600+y^{2} =6400$

$y^{2} =4800$

$\sqrt{y^{2} } =\sqrt{4800}$

$y=40\sqrt{3}$

35.

First use Sin to find $x$

$sin(30)=\frac{x}{15}$

$15*sin(30)=x$

$x=7.5$

Then use the pythagorean theorem to find $y$

$7.5^{2}+ y^{2} =15^{2}$

$56.25+y^{2} =225$

$y^{2} =168.75$

$\sqrt{y^{2} }=\sqrt{168.75}$

$y=\frac{15\sqrt{3} }{2}$