An airplane is flying at an altitude of 8.5 km. it’s angle of elevation from the observer on the ground is 35°. what trigonometric ratio will be able to determine the horizontal distance between the observer and the airplane?
Question: An airplane is flying at an altitude of 8.5 km. it’s angle of elevation from the observer on the ground is 35°. what trigonometric ratio will be able to determine the horizontal distance between the observer and the airplane?
To determine the horizontal distance between the observer on the ground and the airplane, we can use the trigonometric ratio of tangent (tan).
In this scenario, the opposite side is the altitude of the airplane (8.5 km), and the adjacent side is the horizontal distance we want to find. The angle of elevation is given as 35°.
Using the tangent function:
tan(angle) = opposite/adjacent
tan(35°) = 8.5 km/adjacent
To find the adjacent side (horizontal distance), we rearrange the equation:
adjacent = opposite/tan(angle)
adjacent = 8.5 km/tan(35°)
Now, we can calculate the value using a calculator:
adjacent ≈ 8.5 km / 0.7002
adjacent ≈ 12.139 km
Therefore, the horizontal distance between the observer and the airplane is approximately 12.139 kilometers.
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