Answer :
Final answer:
The length of the other taxiway can be found using the Law of Cosines.
Explanation:
The problem can be solved using the Law of Cosines. The length of the other taxiway can be found using the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where:
c is the length of the other taxiway
a is the length of the runway (6400 ft)
b is the length of the given taxiway (3700 ft)
C is the angle between the runway and the given taxiway (69°).
Plugging in the known values, we get:
c^2 = (6400)^2 + (3700)^2 - 2 * 6400 * 3700 * cos(69°)
Solving this equation will give us the length of the other taxiway. Round the answer to three significant digits.
Learn more about geometry
Final answer:
To find the length of the other taxiway, use the Law of Cosines with given values. The length of the other taxiway is approximately 819 ft.
Explanation:
To find the length of the other taxiway, we can use the Law of Cosines, which states that in a triangle, [tex]c^2 = a^2 + b^2[/tex] - 2ab·cos(C), where c is the length of the side opposite angle C. In this case, the runway is side c, and the given taxiway is side a. Let's denote the length of the other taxiway as b. We can use the equation:
[tex]b^2 = 6400^2 + 3700^2[/tex] - 2(6400)(3700)cos(69.0)
[tex]b^2[/tex] = 40960000 + 13690000 - 2(23680000)cos(69.0)
[tex]b^2[/tex] = 54650000 - 47360000cos(69.0)
[tex]b^2[/tex] ≈ 6704149.145
b ≈ [tex]\sqrt{6704149.145}[/tex]
b ≈ 819.204
Rounding to three significant digits, the length of the other taxiway is approximately 819 ft.
