Question

solve for the value of x. rc
a)

Explanation:

Step1: Identify triangle properties

The figure shows an isosceles triangle (marked sides equal) within right triangle $WVU$, so $\angle WUV = \angle UWX$. First, find $\angle U$ in $\triangle WVU$:
$\angle U = 90^\circ - 68^\circ = 22^\circ$

Step2: Apply Law of Sines

In the triangle with sides $x$, 96, and angles $68^\circ$, $22^\circ$:
$\frac{x}{\sin(22^\circ)} = \frac{96}{\sin(68^\circ)}$

Step3: Solve for $x$

Rearrange to isolate $x$:
$x = \frac{96 \times \sin(22^\circ)}{\sin(68^\circ)}$
Calculate $\sin(22^\circ) \approx 0.3746$, $\sin(68^\circ) \approx 0.9272$:
$x \approx \frac{96 \times 0.3746}{0.9272} \approx 38.8$

Answer:

$x \approx 38.8$