Question

2 0/1 point x = 21.85

Explanation:

Step1: Find the third - angle of the triangle

The sum of interior angles of a triangle is 180°. Let the third - angle be $\theta$. Then $\theta=180-(64 + 87)=29^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we have $\frac{x}{\sin64^{\circ}}=\frac{45}{\sin87^{\circ}}$.

Step3: Solve for $x$

$x=\frac{45\times\sin64^{\circ}}{\sin87^{\circ}}$. Since $\sin64^{\circ}\approx0.8988$ and $\sin87^{\circ}\approx0.9986$, then $x=\frac{45\times0.8988}{0.9986}\approx40.4$.

Answer:

$x\approx40.4$