Question

2 fill in the blank 1 point x = 21.84 previous

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ for a triangle with sides $a,b,c$ and opposite angles $A,B,C$ respectively. Here we have $\frac{x}{\sin64^{\circ}}=\frac{45}{\sin87^{\circ}}$.

Step2: Solve for $x$

Cross - multiply to get $x=\frac{45\times\sin64^{\circ}}{\sin87^{\circ}}$. We know that $\sin64^{\circ}\approx0.8988$ and $\sin87^{\circ}\approx0.9986$. Then $x=\frac{45\times0.8988}{0.9986}=\frac{40.446}{0.9986}\approx40.5$.

Answer:

$40.5$