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SOH-CAH-TOA Practice Worksheet

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SOH-CAH-TOA Practice Worksheet

Right-angled triangle diagram

📚 Part 1: SOH-CAH-TOA Basics

Remember: SOH = Sine = Opposite ÷ Hypotenuse | CAH = Cosine = Adjacent ÷ Hypotenuse | TOA = Tangent = Opposite ÷ Adjacent

1. In a right-angled triangle, if the opposite side is 3cm and the hypotenuse is 5cm, what is sin θ?

3/5

5/3

3/4

4/5

2. If the adjacent side is 4cm and the hypotenuse is 8cm, what is cos θ?

1/2

2/1

4/8

Both A and C

3. Which ratio would you use to find an angle when you know the opposite and adjacent sides?

Sine

Cosine

Tangent

✏️ Part 2: Calculating Angles

4. Find angle θ when the opposite side = 6cm and the adjacent side = 8cm.

Step 1: Choose the correct ratio: tan θ = ____________

Step 2: Calculate: tan θ = _____ ÷ _____ = _____

Step 3: Find the angle: θ = tan⁻¹(____) = _____°

5. Find angle θ when the opposite side = 5cm and the hypotenuse = 13cm.

Step 1: Choose the correct ratio: _____ θ = ____________

Step 2: Calculate: _____ θ = _____ ÷ _____ = _____

Step 3: Find the angle: θ = _____⁻¹(____) = _____°

🔧 Part 3: Problem Solving

6. A ladder leans against a wall. The ladder is 10m long and makes an angle of 60° with the ground. How high up the wall does the ladder reach?

Which ratio will you use? ________________

Set up your equation: ________________

Calculate: Height = _______ metres

7. From the top of a 20m tall building, the angle of depression to a car is 30°. How far is the car from the base of the building?

Which ratio will you use? ________________

Set up your equation: ________________

Calculate: Distance = _______ metres

8. Challenge: In triangle ABC, angle C = 90°, side AB = 15cm, and angle A = 40°. Find the length of side BC.

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