An aircraft took off at an angle of 32 degrees. How far had it flown when it reached a (vertical) height of 1200m (nearest metre)?
draw a diagram. Then it will be clear that your distance x can be found by
1200/x = sin32°
To find the distance the aircraft had flown when it reached a vertical height of 1200 meters, we can use trigonometry. In this case, we need to use the tangent function because we have the angle and the opposite side.
We know that the tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the vertical height of 1200 meters, and we need to find the adjacent side, which represents the distance flown by the aircraft.
Using the formula, we have:
tan(angle) = opposite / adjacent
tan(32 degrees) = 1200m / adjacent
To find the adjacent side, we rearrange the formula:
adjacent = opposite / tan(angle)
adjacent = 1200m / tan(32 degrees)
Now we can calculate the value using a calculator or trigonometric tables.
Using a calculator, we have:
adjacent ≈ 1200m / 0.6248693536
adjacent ≈ 1921.32m
Therefore, the aircraft had flown approximately 1921 meters when it reached a vertical height of 1200 meters (nearest meter).