To determine the missile's altitude, we need to use trigonometry. Here are the steps to find the altitude:
1. Convert the speed from miles per hour to miles per minute, since we know the time traveled in minutes. To do this, divide the average speed by 60 (since there are 60 minutes in an hour):
Speed (miles per minute) = 6000 miles/hour ÷ 60 minutes/hour = 100 miles/minute
2. Since we know the speed and time of travel, we can calculate the distance covered by multiplying the speed by time:
Distance = Speed × Time = 100 miles/minute × 2 minutes = 200 miles
3. Next, we can use trigonometry to find the altitude. The vertical distance (altitude) is represented by the opposite side of the angle of 26.5 degrees. The adjacent side represents the horizontal distance traveled.
4. We need to find the opposite side of the triangle. We can use the sine function to calculate this value:
Sin(26.5°) = Opposite / Hypotenuse
We know the hypotenuse is the distance covered (200 miles), so we can rearrange the equation to solve for the opposite side (altitude):
Opposite = Sin(26.5°) × Hypotenuse
Opposite = Sin(26.5°) × 200 miles
5. Finally, calculate the value of the opposite (altitude):
Altitude = Sin(26.5°) × 200 miles
Using a calculator, find Sin(26.5°) and multiply it by 200 miles to determine the missile's altitude.