Solving Right Triangles Using SOH, CAH, and TOA

Introduction

• The lecture focuses on solving missing parts of right triangles using trigonometric ratios: SOH, CAH, and TOA.
• SOH, CAH, TOA are acronyms for the trigonometric ratios related to right triangles.

SOH, CAH, TOA Definitions

• SOH: Sine = Opposite / Hypotenuse
• CAH: Cosine = Adjacent / Hypotenuse
• TOA: Tangent = Opposite / Adjacent

Example 1

• Given: A right triangle with a 36° acute angle.
• Objective: Find the missing side (X), which is the opposite side to the 36° angle.
• Information:
  • Hypotenuse = 10 cm
  • Missing side = Opposite to the 36° angle
• Solution:
  • Use the SOH formula: Sine = Opposite / Hypotenuse.
  • Equation: ( \sin(36°) = \frac{X}{10} )
  • Cross-multiply to find X: ( X = 10 \times \sin(36°) )
  • Calculate using a calculator: ( X \approx 5.9 \text{ cm} )

Example 2

• Given: A right triangle with a 40° acute angle.
• Objective: Find the missing side (X), which is the opposite side to the 40° angle.
• Information:
  • Adjacent side = 6 cm
  • Missing side = Opposite to the 40° angle
• Solution:
  • Use the TOA formula: Tangent = Opposite / Adjacent.
  • Equation: ( \tan(40°) = \frac{X}{6} )
  • Cross-multiply to find X: ( X = 6 \times \tan(40°) )
  • Calculate using a calculator: ( X \approx 5 \text{ cm} )

Exercise

• Draw a right triangle with:
  • Given angle: 34°
  • Given side: 12 cm
  • Find the missing side.
• Students are encouraged to solve and comment their answer.

Conclusion

• Emphasis on the importance of using trigonometric ratios to solve for missing sides in right triangles.
• Encouragement to practice by solving the provided exercise.

Additional Notes

• The use of a scientific calculator is essential for solving these problems.
• Final answers are expressed to one decimal place or as whole numbers after rounding.
• Students are encouraged to participate and engage by commenting answers.