Question

An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)? plzzz helpppp

Answer 1

Rule 1 when solving these: Draw a picture

I used the simplest geometry I could (wasn't sure what level of mathematics you were).

If the picture doesn't come through I'm sorry.

Final answer is 291.10936206249 miles or approximately 291 miles.

Answer 2

Answer:

Distance between plane and airport is 134.4 miles.

Step-by-step explanation:

Given : An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W.

To find : How far is the plane from the airport.

Solution : Distance from airport to west is 150 miles and then 170 miles in the direction south  and angle form is S 49.17° W

Refer the attached picture for clearance.

Applying law of cosines

$c^2=a^2+b^2-2ab Cos(C)$

$c=\sqrt{a^2+b^2-2ab Cos(C)}$

where a= 150 miles

b=170 miles

C=   49.17° angle in degree

c = distance between plane from the airport

Put values in the formula,

$c=\sqrt{a^2+b^2-2ab Cos(C)}$

$c=\sqrt{150^2+170^2-2(150)(170) Cos(49.17^{\circ})}$

$c=\sqrt{22500+28900-51000(0.653)}$

$c=\sqrt{51400-33303}$

$c=\sqrt{18057}$

$c=134.37$

Therefore, Distance between plane and airport is 134.4 miles.