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qaws [65]
3 years ago
7

a pilot flying at In altitude of 1800 m spots in airplane in the distance he notices that the angle of the depression from the p

lane to the airport is 22° how far is the plane from the airport in altitude of 1800 m spots an airplane in the distance he notices that the angle of the depression from the plane to the airport is 22° how far is the plane from the airport
Mathematics
1 answer:
kogti [31]3 years ago
7 0
Let x be the distance between the plane and the airport.
We have,
Angle of depression = 22°
Altitude = 1800 m
Sin 22° = Opposite/Hypotenuse
=> Sin 22° = Altitude/x
=> Sin 22° = 1800/x
=> x × Sin 22° = 1800
=> x = 1800/Sin 22°
=> x = 1800/0.3746065934
=> x = 4805.04089 m
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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
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  3. Exponents
  4. Multiplication
  5. Division
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  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

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Step-by-step explanation:

<u>Step 1: Define</u>

Leg <em>a</em> = 8

Leg <em>b</em> = 4

Hypotenuse <em>c</em> = <em>x</em>

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute in variables [Pythagorean Theorem]:                                            8² + 4² = x²
  2. Evaluate exponents:                                                                                         64 + 16 = x²
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  4. [Equality Property] Square root both sides:                                                    √80 = x
  5. Rewrite:                                                                                                             x = √80
  6. Simplify:                                                                                                             x = 4√5
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