Question

2. A 30-60-90 triangle has a hypotenuse of 10. Use special right triangle formulas to find the long side. Explain your work.

Answer 1

Given:

The angles of the triangle are in the order 30-60-90.

The hypotenuse side is 10.

To find:

The long side.

Explanation:

Let us draw the triangle.

Using the trigonometric ratio formula,

$\begin{gathered} \sin\theta=\frac{Opp}{Hyp} \\ sin30^{\circ}=\frac{Opp}{10} \\ \frac{1}{2}=\frac{Opp}{10} \\ Opp=5 \end{gathered}$

Using the trigonometric ratio formula,

$\begin{gathered} cos\theta=\frac{Adj}{Hyp} \\ cos60^{\circ}=\frac{adj}{10} \\ \frac{\sqrt{3}}{2}=\frac{adj}{10} \\ adj=5\sqrt{3} \\ adj=8.66 \end{gathered}$

Comparing the three sides, the longest side will be the hypotenuse side.

That is side 10.

Final answer:

The longest side is the hypotenuse side of 10.