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Find z and y..no decimals just exact answers

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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

Find z and y..no decimals just exact answers-example-1
User Marmeladze
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