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SOH-COH-TOA Practice Problems

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SOH-COH-TOA Practice Problems

Right-angled triangle with SOH-COH-TOA labels

📐 Part 1: Finding Trigonometric Ratios

Remember: SOH-COH-TOA stands for:

Sine = Opposite ÷ Hypotenuse

Cosine = Adjacent ÷ Hypotenuse

Tangent = Opposite ÷ Adjacent

1. Given a right-angled triangle where the opposite side is 7 cm and the hypotenuse is 25 cm, find sin θ.

Which ratio do I use? ________________

sin θ = ________________

2. A triangle has an adjacent side of 12 cm and a hypotenuse of 13 cm. Calculate cos θ.

Which ratio do I use? ________________

cos θ = ________________

3. The opposite side measures 5 cm and the adjacent side is 12 cm. Find tan θ.

Which ratio do I use? ________________

tan θ = ________________

🔍 Part 2: Finding Angles and Lengths

4. Using a triangle with an opposite side of 8 cm and hypotenuse 17 cm, find the angle θ (to the nearest degree) using sine inverse.

Step 1: sin θ = _______ ÷ _______ = _______

Step 2: θ = sin⁻¹(_______) = _______°

5. In a right-angled triangle, the opposite side is 6 cm and θ = 35°. Use sine to find the length of the hypotenuse.

Step 1: sin(35°) = _______ ÷ hypotenuse

Step 2: Rearrange to find hypotenuse = _______

Hypotenuse = _______ cm (to 1 decimal place)

6. Challenge: In a right-angled triangle, if θ = 30° and the adjacent side is 10 cm, find the length of the hypotenuse using cosine.

Step 1: cos(30°) = _______ ÷ hypotenuse

Step 2: Rearrange to find hypotenuse = _______

Hypotenuse = _______ cm (to 1 decimal place)

💭 Part 3: Reflection

7. Explain in your own words when you would use each trigonometric ratio. Complete the sentences below:

I use sine when I know the _____________ and _____________ sides.

I use cosine when I know the _____________ and _____________ sides.

I use tangent when I know the _____________ and _____________ sides.

8. What is the most important thing to remember when identifying the opposite and adjacent sides?

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