What is SOH CAH TOA?
SOH CAH TOA is a mnemonic device used to remember the basic trigonometric ratios in a right triangle. Each part stands for a ratio between two sides of a right triangle:
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
This is useful when dealing with right triangles, especially when you know one angle (other than the right angle) and one side, and want to find the other sides or angles.
Breaking Down the Mnemonic
1. SOH:
\[ \sin(\theta) = \frac{\text{Opposite side}}{\text{Hypotenuse}} \]
2. CAH:
\[ \cos(\theta) = \frac{\text{Adjacent side}}{\text{Hypotenuse}} \]
3. TOA:
\[ \tan(\theta) = \frac{\text{Opposite side}}{\text{Adjacent side}} \]
Where \( \theta \) (theta) is the angle in question.
Example sa Real Life: Pag-akyat ng Bubong
Halimbawa, si Mang Tonyo ay aakyat sa bubong gamit ang hagdan. Ang hagdan ay 5 meters ang haba at nakasandal sa bahay sa angle na 60° mula sa lupa. Gamit ang SOH CAH TOA, maaari nating malaman kung gaano kataas ang inakyat ni Mang Tonyo.
Given:
- Hypotenuse (hagdan) = 5 m
- Angle \( \theta = 60^\circ \)
Gamit ang SOH:
\[ \sin(60^\circ) = \frac{\text{Opposite}}{5} \]
\[ \text{Opposite} = 5 \times \sin(60^\circ) \approx 5 \times 0.866 = 4.33 \text{ meters} \]
Ibig sabihin, ang taas ng naakyat ni Mang Tonyo ay mga 4.33 meters.
Another Example: Shadow ng Posteng Panlabas
May poste sa kalsada na nagpapakita ng shadow sa tanghali. Kung alam natin na ang anggulo ng araw mula sa lupa ay 45° at ang haba ng shadow ay 3 meters, gaano kataas ang poste?
Given:
- Angle = 45°
- Adjacent (shadow) = 3 m
Gamit ang TOA:
\[ \tan(45^\circ) = \frac{\text{Opposite}}{3} \]
\[ \text{Opposite} = 3 \times \tan(45^\circ) = 3 \times 1 = 3 \text{ meters} \]
Ang taas ng poste ay 3 meters.
Summary
Use SOH CAH TOA to solve right triangle problems by remembering:
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
This is extremely helpful in real-world problems involving ladders, buildings, shadows, ramps, and more.
