Question

Find z and y..no decimals just exact answers

Answer 1

Triangle is a right triangle because has a 90° angle

then we can use trigonometric ratios to find sides

if I use sine

`\sin (\alpha)=(O)/(H)`

whre alpha is the reference angle, O the opposite side to the angle and h the hypotenuse of the triangle

using 60° as reference angle

`\sin (60)=\frac{x}{4\sqrt[]{3}}`

then solve for x

`\begin{gathered} x=4\sqrt[]{3}\sin (60) \\ \\ x=6 \end{gathered}`

the value of side x is 6 units

If I use cosine

`\cos (\alpha)=(A)/(H)`

where alpha is the reference angle, a the adjacent side to the references angle and H the hypotenyse of the triangle

using 60° as reference angle

`\cos (60)=\frac{y}{4\sqrt[]{3}}`

then solve for y

`\begin{gathered} y=4\sqrt[]{3}\cos (60) \\ \\ y=2\sqrt[]{3} \end{gathered}`

the value of side x is 2root3 units