Question

What operation(s) would you perform on the longer leg (across from the 60 degree angle) of a 30-60-90 triangle to get the length of the hypotenuse?Multiply by v2.Divide by 2.Divide by V3, multiply by 2Divide by 2, multiply by 2.

Answer 1

We have a 30-60-90 triangle.

From the picture of about we can say that respect to the angle θ=30° we have that:

- H = hyptotenuse = Green side

- AC = Red side = adjacent cathetus = longer leg

- OC = Blue side = opposite cathetus

Now, we want to find the hypotenuse (H) in terms of the longer leg (AC, the adjacent cathetus).

We can apply the following trigonometric relation:

$\begin{gathered} \cos \theta=\frac{AC}{H} \\ \cos (30^{\circ})=\frac{AC}{H} \\ H\cdot\cos (30^{\circ})=AC \\ H=\frac{AC}{\cos (30^{\circ})} \end{gathered}$

Now, replacing the value of cos(30°) = √3 / 2 we find that:

$H=\frac{AC}{cos(30^{\circ})}=\frac{AC}{\frac{\sqrt[]{3}}{2}}=\frac{2}{\sqrt[]{3}}\cdot AC$

Answer

We find the length of the hypotenuse dividing by √3 and multiplying by 2 the longer leg.