Question

5 fill in the blank 1 point a pilot flying over the norfolk airport is told he will have to redirect and land in either richmond or raleigh. due to air traffic, he is then told he must land in raleigh. find the distance he will travel. richmond 139 mi 83° norfolk 31° raleigh 267.9 mi

Explanation:

Step1: Use the Law of Sines

Let the distance from Norfolk to Raleigh be $x$. In a triangle with sides and angles, by the Law of Sines, $\frac{x}{\sin83^{\circ}}=\frac{139}{\sin31^{\circ}}$.

Step2: Solve for $x$

$x = \frac{139\times\sin83^{\circ}}{\sin31^{\circ}}$. Since $\sin83^{\circ}\approx0.9925$ and $\sin31^{\circ}\approx0.5150$, then $x=\frac{139\times0.9925}{0.5150}=\frac{137.9575}{0.5150}\approx267.9$ mi.

Answer:

$267.9$ mi