SOH-CAH-TOA is a mnemonic device used to remember the basic trigonometric ratios which are essential for solving missing sides and angles in a right triangle.
It is derived from the AA Similarity Postulate which states that the ratios of the lengths of two sides of similar right triangles are equal.
Definition of SOH-CAH-TOA
SOH: Sin(θ) = Opposite / Hypotenuse
CAH: Cos(θ) = Adjacent / Hypotenuse
TOA: Tan(θ) = Opposite / Adjacent
Importance
These trigonometric ratios hold true for all right triangles, irrespective of their size.
They are crucial for determining missing measurements in triangles.
Remembering Trig Functions
Mnemonic Sayings:
"Some Of Her Children Are Having Trouble Over Algebra"
"Oscar Had A Heap Of Apples"
Triangle Sides Labeling:
Opposite Leg: The side opposite the acute angle.
Adjacent Leg: The side next to the acute angle but not the hypotenuse.
Hypotenuse: The longest side, opposite the right angle.
Application
Used to solve for unknown sides or angles in right triangles using the trigonometric ratios.
Inverse Trig Ratios are used to find missing angles when two side lengths are known.
Common Questions
Applicability: SOH-CAH-TOA is only applicable to right triangles.
Usage: Utilized when two sides of a right triangle are known and the third side or angles need to be calculated.
Hypotenuse Position: Opposite to the 90-degree angle and the longest side.
Adjacent Side: The side touching the angle but not the hypotenuse.
Solving a Right Triangle: Involves finding all missing sides and angles using trig ratios, triangle sum theorem, and/or Pythagorean theorem.
Video Lesson Highlights
Duration: 1 hr 34 min
Breakdown:
Intro to Trigonometric Ratios
Understanding SOH-CAH-TOA
Finding Trig Ratios for Acute Angles
Completing Tables Using SOH-CAH-TOA
Solving Angles with a Calculator
Solving Right Triangles
Application in Word Problems
Finding Unknowns Using SOH-CAH-TOA
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