Question
4.) A person whose eyes are 5 feet above the ground is stanind on the runway of an airport 100 feet
from the control tower. That person observes an air traffic controller at the window of the 132
foot tower. What is the angle of elevation?
from the control tower. That person observes an air traffic controller at the window of the 132
foot tower. What is the angle of elevation?
Ask by Moran Grant. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The angle of elevation is approximately 51.8 degrees.
Solution
To determine the angle of elevation, we’ll analyze the right triangle formed by the observer’s eye level, the horizontal distance to the control tower, and the height difference between the observer and the top of the tower.
Given:
- Horizontal distance (adjacent side): 100 feet
- Height of the control tower: 132 feet
- Height of the observer’s eyes above the ground: 5 feet
Step-by-Step Solution:
-
Calculate the vertical difference (opposite side):
-
Use the tangent function to find the angle of elevation (
): -
Find the angle whose tangent is 1.27:
-
Calculate
:
Using a calculator,
Conclusion:
The angle of elevation from the observer’s eye level to the top of the control tower is approximately 51.8 degrees.
Answer:
The angle of elevation is approximately 51.8 degrees.
The angle of elevation is approximately 51.8 degrees.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To find the angle of elevation, you can visualize a right triangle where the height of the tower above the observer’s eye level is 132 feet - 5 feet = 127 feet, and the distance from the observer to the tower is 100 feet. The angle of elevation (θ) can be calculated using the tangent function:
tan(θ) = opposite / adjacent = 127 / 100.
Thus, θ = arctan(127/100), which gives you approximately 51.3 degrees!
Thus, θ = arctan(127/100), which gives you approximately 51.3 degrees!
Now, that’s not just number crunching; you’re employing some nifty trigonometry to connect the math to the real world of airports and air traffic control. Math isn’t just for classrooms; it’s what keeps our skies safe!