Question

Match the variable to its correct length please

Answer 1

`x=10`

`y=20`

Explanation:

Note:

(sin, cos, tan) Formulas:

`sin(\theta)=(opposite)/(hypotenuse)`

`cos(\theta)=(adjacent)/(hypotenuse)`

`tan(\theta)=(opposite)/(adjacent)`

To find the value of
`x`

1) Using
`tan` formula

`tan(\theta)=(opposite)/(adjacent)`

`tan(60°)=(10√(3))/(x)`

2) Multiply both sides by
`x`

`xtan(60°)=(10√(3))/(x)* x`

`xtan(60°)=10√(3)`

3) Divide both side by
`tan(60°)`

`(xtan(60°))/(tan(60°))=(10√(3))/(tan(60°))`

4) Calculate

`x=(10√(3))/(tan(60°))`

`x=10`

To find the value of
`y`

1) Using
`cos` formula

`cos(\theta)=(adjacent)/(hypotenuse)`

`cos(60°)=(10)/(y)`

2) Multiply both sides by
`y`

`ycos(60°)=(10)/(y)* y`

`ycos(60°)=10`

3) Divide both side by
`cos(60°)`

`(ycos(60°))/(cos(60°))=(10)/(cos(60°))`

4) Calculate

`y=(10)/(cos(60°))`

`y=20`