Question

a small plane lands at a point 324 miles east and 92 miles north of the point at which it took off. Find the distance the plane flew and the direction​

Answer 1

Answer: 336.80 miles, $15.85^{\circ}$ North of east

Step-by-step explanation:

Given

Plane lands at a point 324 miles east and 92 miles north

Distance is given by using Pythagoras theorem

$\Rightarrow d=\sqrt{324^2+92^2}\\\\\Rightarrow d=\sqrt{113,440}\\\\\Rightarrow d=336.80\ \text{miles}$

Direction is given by using figure i.e.

$\Rightarrow \tan \theta=\dfrac{92}{324}\\\\\Rightarrow \tan \theta=0.2839\\\\\Rightarrow \theta=15.85^{\circ}$

Direction is $15.85^{\circ}$ North of east