Question

which of the following equations could be used to find the value of x? the figure is not drawn to scale answer $\frac{sin(x)}{25}=\frac{sin(36)}{51}$ $\frac{sin(x)}{69}=\frac{sin(36)}{25}$ $cos x=\frac{51^{2}+25^{2}-69^{2}}{2(51)(25)}$ $cos x=\frac{25^{2}+69^{2}-51^{2}}{2(25)(69)}$

Explanation:

Step1: Recall the Law of Sines

The Law of Sines states that in a triangle, $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$, where $A$, $B$, $C$ are angles and $a$, $b$, $c$ are the lengths of the sides opposite those angles.

Step2: Identify the relevant sides and angles

We have an angle of $36^{\circ}$ with opposite - side length $51$ and an angle of $x^{\circ}$ with opposite - side length $25$.

Step3: Apply the Law of Sines

Using the Law of Sines, we get $\frac{\sin(x)}{25}=\frac{\sin(36)}{51}$.

Answer:

$\frac{\sin(x)}{25}=\frac{\sin(36)}{51}$