Question

multiple choice
for exercises 1-6, choose the correct letter.

1. what is the value of \\(sin n\\)?

\\(\boldsymbol{\text{a}}\\) \\(\frac{1}{2}\\) \\(\boldsymbol{\text{c}}\\) \\(\frac{\sqrt{3}}{2}\\)
\\(\boldsymbol{\text{b}}\\) \\(\frac{\sqrt{3}}{3}\\) \\(\boldsymbol{\text{d}}\\) \\(\sqrt{3}\\)
(there is a right triangle \\(nop\\) with right angle at \\(o\\), (no = 5), (op = 5\sqrt{3}), (np = 10))

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for $\angle N$

For $\angle N$, opposite side is $OP = 5\sqrt{3}$, hypotenuse is $NP = 10$.

Step3: Calculate $\sin N$

$\sin N=\frac{OP}{NP}=\frac{5\sqrt{3}}{10}=\frac{\sqrt{3}}{2}$

Answer:

C. $\frac{\sqrt{3}}{2}$