Question

Find the value of the hypotenuse in the triangleshown:1230°O6V3O 8V3O 123O 243

Answer 1

We know that in a right triangle the cossine of an angle if giving by the formula:

`\cos (\alpha)=(adjacent)/(Hypotenuse)`

We also know that:

`\cos (30\degree)=\frac{\sqrt[]{3}}{2}`

Using those information in our triangle, we find:

`\cos (30\degree)=(12)/(Hypotenuse)\text{ }\Rightarrow\text{ }\frac{\sqrt[]{3}}{2}=(12)/(Hypotenuse)\text{ }\Rightarrow\text{ }Hypotenuse=\frac{12*2}{\sqrt[]{3}}`

Continuing with the algebra, we find:

`Hypotenuse=\frac{24}{\sqrt[]{3}}*\frac{\sqrt[]{3}}{\sqrt[]{3}}\text{ = }\frac{24\sqrt[]{3}}{3}\text{ = 8}\sqrt[]{3}`

So, our Hypotenuse is:

`Hypotenuse\text{ = 8}\sqrt[]{3}`