Question 1171875: A plane took off with an angle of elevation \thetaθ. After the plane had traveled 4,540 feet horizontally, it was 10,000 feet above the ground. What was the angle of elevation of the plane? Round to the nearest degree.
Answer by math_tutor2020(3817)   (Show Source):
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Draw a right triangle with horizontal leg 4540 and vertical leg 10,000. The angle of elevation, theta, is the acute angle formed between the horizontal leg and the hypotenuse.
Use the tangent rule to connect the two legs of the triangle
tan(angle) = opposite/adjacent
tan(theta) = (vertical leg)/(horizontal leg)
tan(theta) = (10,000)/(4540)
tan(theta) = 2.20264317180617
Apply the arctangent, or inverse tangent, to both sides to isolate theta
tan(theta) = 2.20264317180617
arctan(tan(theta)) = arctan(2.20264317180617)
theta = arctan(2.20264317180617)
theta = 65.5819513728353
Make sure your calculator is in degree mode.
This theta value rounds to theta = 66 when rounding to the nearest degree.
Answer: about 66 degrees
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