Question

question starting from an airport, an airplane flies 200 miles southwest, then 225 miles west. how far, in miles, from the airport is the plane? (round your answer to the nearest hundredth if necessary.) provide your answer below: miles

Explanation:

Step1: Resolve southwest - component

The southwest direction is at a 45 - degree angle. The west - component of the 200 - mile southwest flight is $200\cos45^{\circ}=200\times\frac{\sqrt{2}}{2}=100\sqrt{2}\approx141.42$ miles, and the south - component is also $100\sqrt{2}\approx141.42$ miles. The total west - direction distance is $d_{west}=141.42 + 225=366.42$ miles, and the south - direction distance is $d_{south}=141.42$ miles.

Step2: Use the Pythagorean theorem

The distance $d$ from the starting - point (airport) to the final position of the plane is given by $d=\sqrt{d_{west}^{2}+d_{south}^{2}}$. Substitute $d_{west}=366.42$ miles and $d_{south}=141.42$ miles into the formula: $d=\sqrt{(366.42)^{2}+(141.42)^{2}}=\sqrt{134263.6164 + 19999.6164}=\sqrt{154263.2328}\approx372.06$ miles.

Answer:

372.06