Question

given right triangle xyz, what is the value of tan(60°)?
options:
√3
√3/2
1/2
2/1

Explanation:

Step1: Recall Tangent Definition

In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ to angle $\theta$.

Step2: Identify Sides for $60^\circ$

For $\angle X = 60^\circ$:

• Opposite side to $60^\circ$: $YZ$ (let's find its length using Pythagoras or 30-60-90 ratios). In 30-60-90 triangle, hypotenuse is $42$, shorter leg ($XZ$) is $21$, so longer leg ($YZ$) is $21\sqrt{3}$.
• Adjacent side to $60^\circ$: $XZ = 21$.

Step3: Calculate $\tan(60^\circ)$

$\tan(60^\circ) = \frac{YZ}{XZ} = \frac{21\sqrt{3}}{21} = \sqrt{3}$.

Answer:

$\sqrt{3}$ (corresponding to the first option with $\sqrt{3}$)