Final answer:
To find the height of a hot air balloon given an angle of elevation of 28 degrees from 50 meters away, one can use the tangent function. By calculating tan(28°) and multiplying by 50, the height is determined to be approximately 26.585 meters.
Step-by-step explanation:
To solve the mathematical problem of finding the height of a hot air balloon using the angle of elevation, one can use trigonometric functions. The angle of elevation is given as 28 degrees, and the distance from the observer to the base of the balloon is 50 meters. We apply the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.
In this scenario, the opposite side is the height of the balloon (h), and the adjacent side is the distance from the observer to the balloon's base (50 meters). Thus, tan(28°) = h / 50m. To find the height (h) of the hot air balloon, we rearrange the formula to h = 50m * tan(28°).
Calculation:
h = 50m * tan(28°)
Now, using a calculator with the tangent function, we can determine the height:
tan(28°) ≈ 0.5317
h ≈ 50m * 0.5317
h ≈ 26.585 meters
The height of the hot air balloon is approximately 26.585 meters