Answer:
[tex]x=10[/tex]
[tex]y=20[/tex]
Step-by-step explanation:
Note:
(sin, cos, tan) Formulas:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
To find the value of [tex]x[/tex]
1) Using [tex]tan[/tex] formula
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
[tex]tan(60°)=\dfrac{10\sqrt{3}}{x}[/tex]
2) Multiply both sides by [tex]x[/tex]
[tex]xtan(60°)=\dfrac{10\sqrt{3}}{x}\times x[/tex]
[tex]xtan(60°)=10\sqrt{3}[/tex]
3) Divide both side by [tex]tan(60°)[/tex]
[tex]\dfrac{xtan(60°)}{tan(60°)}=\dfrac{10\sqrt{3}}{tan(60°)}[/tex]
4) Calculate
[tex]x=\dfrac{10\sqrt{3}}{tan(60°)}[/tex]
[tex]x=10[/tex]
To find the value of [tex]y[/tex]
1) Using [tex]cos[/tex] formula
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]cos(60°)=\dfrac{10}{y}[/tex]
2) Multiply both sides by [tex]y[/tex]
[tex]ycos(60°)=\dfrac{10}{y}\times y[/tex]
[tex]ycos(60°)=10[/tex]
3) Divide both side by [tex]cos(60°)[/tex]
[tex]\dfrac{ycos(60°)}{cos(60°)}=\dfrac{10}{cos(60°)}[/tex]
4) Calculate
[tex]y=\dfrac{10}{cos(60°)}[/tex]
[tex]y=20[/tex]
