I need to find side x in its simplest radical form using the special right triangles method
1 answer:
Answer:
\sqrt{6}
Explanation:
From the given diagram,
Hypotenuse sde = x
Opposite side = \sqrt{3}
Using the SOH CAH TOA identity
Sintheta = opposite/hypotenuse
Sin 45 = \sqrt{3}/x
x = \sqrt{3}/sin45
![\begin{gathered} x\text{ =}\frac{\sqrt[]{3}}{\sin 45} \\ x\text{ = }\frac{\sqrt[]{3}}{\frac{1}{\sqrt[]{2}}} \\ x\text{ = }\sqrt[]{3^{}}\cdot\sqrt[]{2} \\ x\text{ =}\sqrt[]{6} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5Ctext%7B%20%3D%7D%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csin%2045%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%5B%5D%7B2%7D%7D%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Csqrt%5B%5D%7B3%5E%7B%7D%7D%5Ccdot%5Csqrt%5B%5D%7B2%7D%20%5C%5C%20x%5Ctext%7B%20%3D%7D%5Csqrt%5B%5D%7B6%7D%20%5Cend%7Bgathered%7D)
Hence the value of x is \sqrt{6}
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