The airplane's path is an illustration of right-triangles
Represent the angle of descent with [tex]\theta[/tex]
The angle of descent, [tex]\theta[/tex] is then calculated using the following tangent identity
[tex]\tan(\theta) = \frac{35000\ feet}{150 \ miles}[/tex]
Convert feet to miles
[tex]\tan(\theta) = \frac{6.6287879\ miles }{150 \ miles}[/tex]
Divide
[tex]\tan(\theta) = 0.0442[/tex]
Take the arc tan of both sides
[tex]\theta = \tan^{-1}(0.0442)[/tex]
Evaluate the arc tan
[tex]\theta = 2.5[/tex]
Hence, the angle of descent is 2.5 degrees
Represent the plane's path with p
The plane's path is calculated using the following Pythagoras theorem
[tex]p^2 = (150\ miles)^2 + (35000\ feet)^2[/tex]
Convert feet to miles
[tex]p^2 = (150\ miles)^2 + (6.6287879\ miles)^2[/tex]
Evaluate
[tex]p^2 = 22543.940829[/tex]
Take the square roots
[tex]p = 150.15[/tex]
Hence, the plane's path is 150.15 miles
Read more about right-triangles at:
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