Respuesta :
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
[tex]c^2=a^2+b^2-2ab Cos(C)[/tex]
[tex]c=\sqrt{a^2+b^2-2ab Cos(C)}[/tex]
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,
[tex]c=\sqrt{a^2+b^2-2ab Cos(C)}[/tex]
[tex]c=\sqrt{150^2+170^2-2(150)(170) Cos(49.17^{\circ})}[/tex]
[tex]c=\sqrt{22500+28900-51000(0.653)}[/tex]
[tex]c=\sqrt{51400-33303}[/tex]
[tex]c=\sqrt{18057}[/tex]
[tex]c=134.37[/tex]
Therefore, Distance between plane and airport is 134.4 miles.
The distance between the plane and the airport is 134.37 miles
Data;
Let
- a = 150miles
- b = 170 miles
- C = 49.17°
- c = ?
Cosine Rule
Using cosine rule
[tex]c^2=a^2+b^2-2abCosC[/tex]
substituting the values into the equation and solve,
[tex]c^2 = 150^2+170^2-(2*150*170cos49.17)\\c^2= 51400-33344.660\\c^2=18055.34\\c = \sqrt{18055.34} \\c = 134.37[/tex]
From the calculations above, the distance between the plane and the airport is 134.37 miles
Learn more on cosine rule here;
https://brainly.com/question/1979489
