An aircraft is timetable to travel from A to B. due to bad weather it flies A to c then C to B , where AC and CB make angle of 27°66° with AB, lf AC=220km.

no idea what you want to know, and your typos make it hard even to understand what you said, but I think that

angle C = 180 - (27+66)
the altitude h = 220 sin27°
and you can figure out the rest.

To solve this problem, we can use the Law of Cosines and the information provided.

1. Draw a triangle ABC, where AB represents the direct route from A to B, AC represents the first leg of the flight from A to C, and CB represents the second leg of the flight from C to B.

2. Label AC as 220 km.

3. We are given that angle ACB is 66° and angle CAB is 27°.

4. Let's find the length of CB using the Law of Cosines:
CB^2 = AC^2 + AB^2 - 2 * AC * AB * cos(angle ACB)
CB^2 = (220)^2 + AB^2 - 2 * 220 * AB * cos(66°)
CB^2 = 48400 + AB^2 - 440 * AB * cos(66°) (Equation 1)

5. Now, let's find the length of AB using the Law of Cosines:
AB^2 = AC^2 + CB^2 - 2 * AC * CB * cos(angle CAB)
AB^2 = 220^2 + CB^2 - 2 * 220 * CB * cos(27°)
AB^2 = 220^2 + CB^2 - 440 * CB * cos(27°) (Equation 2)

6. Since we have two unknowns (AB and CB), we need to simultaneous solve Equations 1 and 2. Let's substitute Equation 1 into Equation 2:
AB^2 = 220^2 + (48400 + AB^2 - 440 * AB * cos(66°)) - 440 * (48400 + AB^2 - 440 * AB * cos(66°)) * cos(27°)

7. Simplify the equation:
AB^2 = 220^2 + 48400 + AB^2 - 440 * AB * cos(66°) - 440 * (48400 + AB^2 - 440 * AB * cos(66°)) * cos(27°)

8. Expand and simplify further:
AB^2 = 48320 + 90720 * cos(66°) - 48400 * cos(27°) - 184800 * cos(66°) * cos(27°)

9. Rearrange the equation to solve for AB:
AB^2 - AB^2 + 184800 * cos(66°) * cos(27°) = 48320 - 48400 - 90720 * cos(66°) + 184800 * cos(66°) * cos(27°)

10. Simplify and isolate AB:
AB = sqrt((48320 - 48400 - 90720 * cos(66°) + 184800 * cos(66°) * cos(27°)) / (1 - cos(66°) * cos(27°)))

11. Use a calculator to plug in the values and solve for AB.

Note that this solution assumes a flat surface and neglects other factors that may affect the actual flight path in a real-life scenario (such as wind patterns or specific aircraft limitations).

To solve this problem, we can use trigonometry and the given information to find the distance between points A and B.

Step 1: Draw a diagram to represent the situation. Label points A, B, and C, and the distances AC and CB.

Step 2: We are given that the angles ACB and BAC are 27° and 66°, respectively. Label these angles on the diagram.

Step 3: Since we know the angle BAC and the length of the side AC, we can use the sine function to find the length of the side AB.

Step 4: Recall that the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the side opposite angle BAC is AB, and the hypotenuse is AC.

Step 5: Using the sine function, we can set up the equation: sin(BAC) = AB/AC.

Step 6: Substitute the given values into the equation: sin(66°) = AB/220km.

Step 7: Solve the equation for AB. Multiply both sides of the equation by AC: AB = sin(66°) * 220km.

Step 8: Use a calculator to find the value of sin(66°), which is approximately 0.9135.

Step 9: Multiply 0.9135 by 220km: AB ≈ 200.97km.

Therefore, the distance between points A and B, which is the total distance traveled by the aircraft, is approximately 200.97 kilometers.