Question

#13 find the values of x and y write your answer in simplest form

Answer 1

Given:

Find-:

The value of x and y

Explanation-:

In triangle ABC

`\begin{gathered} AB=\text{ Base} \\ \\ BC=\text{ Perpendicular} \\ \\ AC=\text{ Hypotenuse} \end{gathered}`

Use trignometric property:

`\begin{gathered} \sin\theta=\frac{\text{ Perpendicular}}{\text{ Hypotenuse}} \\ \\ \cos\theta=\frac{\text{ Base}}{\text{ Hypotenuse}} \end{gathered}`

For the value of "y" is:

`\begin{gathered} \sin\theta=\frac{\text{ Perpendicular}}{\text{ Hypotenuse}} \\ \\ \sin60=(BC)/(AC) \\ \\ \sin60=(5)/(y) \\ \\ y=(5)/(\sin60) \end{gathered}`

Value of "Y" is:

`\begin{gathered} y=(5)/(\sin60) \\ \\ y=(5)/((√(3))/(2)) \\ \\ y=(10)/(√(3)) \\ \\ y=(10)/(√(3))*(√(3))/(√(3)) \\ \\ y=(10√(3))/(3) \end{gathered}`

The value of "x" is:

`\begin{gathered} \cos60=\frac{\text{ Base}}{\text{ Hypotenuse}} \\ \\ \cos60=(x)/(y) \\ \\ (1)/(2)=(x)/((10√(3))/(3)) \\ \\ (1)/(2)=(3x)/(10√(3)) \\ \\ (10√(3))/(2*3)=x \\ \\ x=(5√(3))/(3) \\ \\ \end{gathered}`