MATHEMATICS

• Angle of elevation

  Above eye level
• Angle of depression

  Below eye level
• Horizontal line

  Line of sight
• Trigonometry


  The branch of mathematics that deals with the relation between the sides and angles of a triangle
• Right triangle trigonometry


  Used to find the length of one side or the measure of an acute angle of a right triangle
• Right triangle


  • Hypotenuse is the side opposite the right angle and the longest side
  • Opposite side is the side opposite an angle
  • Adjacent side is the side which is also a side of the angle
• Six trigonometric ratios


  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
• Sine


  Opposite side over hypotenuse
• Cosine


  Adjacent side over hypotenuse
• Tangent


  Opposite side over adjacent side
• Cosecant


  Hypotenuse over opposite side (reciprocal of sine)
• Secant


  Hypotenuse over adjacent side (reciprocal of cosine)
• Cotangent


  Adjacent side over opposite side (reciprocal of tangent)
• Finding the six trigonometric ratios of an acute angle in a right triangle

  1. Identify the opposite, adjacent, and hypotenuse sides

  2. Apply the formulas for sine, cosine, and tangent

  3. Calculate the reciprocals for cosecant, secant, and cotangent
• Finding the missing side in a right triangle using the Pythagorean theorem

  1. Identify the known sides

  2. Use the formula c^2 = a^2 + b^2 to solve for the missing side

  3. Take the square root of the result to find the missing side
• Trigonometric ratios


  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
• Pythagorean theorem: c^2 = a^2 + b^2
• Rationalizing the denominator by multiplying numerator and denominator by square root
• Trigonometric ratios


  The ratios between the sides of a right triangle
• Equilateral triangle


  • All sides are equal
  • All angles are 60°
• Perpendicular bisector


  A line that passes through the midpoint of a line segment and is perpendicular to it
• In an equilateral triangle, the perpendicular bisector divides the side into two equal parts
• Triangles with 45-45-90 degree angles have equal side lengths
• The hypotenuse of a 45-45-90 triangle is √2 times the length of the legs
• Trigonometric ratios


  Used to solve right triangles: sine, cosine, tangent
• Sum of angles in a right triangle is 180 degrees
• Angle of elevation


  The acute angle formed by the horizontal line and the line from the observer's eye to the object that is located higher than the observer
• Angle of depression


  The acute angle formed by the horizontal line and the line of sight of the observer when looking at an object that is located lower than the observer
• Alternate interior angles formed by a transversal are equal
• Tangent = opposite/adjacent
• Trigonon

  Greek word meaning triangle
• Metron

  Greek word meaning to measure
• Trigonometry

  Measurement of triangles
• Acute triangle

  A triangle whose angles are all less than 90°
• Special angles

  Angles with a reference of 30°, 45°, and 60°
• Ratio

  Relationship between two numbers of the same kind
• Trigonometry

  Comes from the greek word trigonometria which means triangle measurement
• Trigonometric ratio

  Is the ratio of the lenghts of two sides of a right triangle
• Angle

  The figure formed by two rays, called the sides of the angle, sharing a common endpoint called the vertex
• Clinometer

  A device used to measure angles of elevation or depression