Question

find the value of x.
answer: x = \boxed{} units
question help: video 1 video 2
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Explanation:

Step1: Find third triangle angle

The sum of angles in a triangle is $180^\circ$. Let the unknown angle be $\theta$.
$\theta = 180^\circ - 23^\circ - 33^\circ = 124^\circ$

Step2: Apply Law of Sines

Relate sides and opposite angles: $\frac{x}{\sin\theta} = \frac{73}{\sin23^\circ}$

Step3: Solve for x

Rearrange to isolate $x$ and calculate.
$x = \frac{73 \times \sin124^\circ}{\sin23^\circ}$
$\sin124^\circ \approx 0.8290$, $\sin23^\circ \approx 0.3907$
$x \approx \frac{73 \times 0.8290}{0.3907} \approx \frac{60.517}{0.3907} \approx 154.9$

Answer:

$155$ (rounded to nearest whole number, or $154.9$ for precise decimal)