SOH-CAH-TOA Triangle Problems

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Date:

Right-angled triangle with trigonometric ratios

📚 Part 1: Understanding SOH-CAH-TOA

Remember: SOH-CAH-TOA helps us remember the trigonometric ratios:

• SOH: sin θ = Opposite ÷ Hypotenuse

• CAH: cos θ = Adjacent ÷ Hypotenuse

• TOA: tan θ = Opposite ÷ Adjacent

1. In a right-angled triangle, if the angle is 30°, the opposite side is 5cm, and the hypotenuse is 10cm, which ratio would you use to verify this relationship?

Sine

Cosine

Tangent

2. To find a missing angle when you know the opposite and adjacent sides, you would use:

sin⁻¹

cos⁻¹

tan⁻¹

3. Which of the following are correct trigonometric ratios? (Select all that apply)

sin θ = Adjacent ÷ Hypotenuse

cos θ = Adjacent ÷ Hypotenuse

tan θ = Opposite ÷ Adjacent

sin θ = Opposite ÷ Hypotenuse

✏️ Part 2: Finding Missing Sides

4. In a right-angled triangle, the angle is 45° and the hypotenuse is 12cm. Find the length of the opposite side. (Use your calculator)

Step 1: Identify the ratio needed: _____________

Step 2: Set up the equation: _____________

Step 3: Solve for the unknown side:

Answer: _______ cm (to 2 decimal places)

5. A ladder leans against a wall at an angle of 60° to the ground. If the ladder is 8 metres long, how high up the wall does it reach?

Answer: _______ metres (to 2 decimal places)

6. In a right triangle, the adjacent side is 15cm and the angle is 35°. Calculate the length of the opposite side.

Answer: _______ cm (to 2 decimal places)

🔍 Part 3: Finding Missing Angles

7. In a right triangle, the opposite side is 7cm and the hypotenuse is 14cm. Find the angle θ.

Step 1: Choose the correct inverse ratio: _____________

Step 2: Set up the equation:

Answer: θ = _______ ° (to 1 decimal place)

8. A ramp has a horizontal distance of 20 metres and rises 3 metres vertically. What is the angle of elevation of the ramp?

Answer: _______ ° (to 1 decimal place)

9. Challenge Problem: From the top of a 50-metre tall building, the angle of depression to a car on the ground is 25°. How far is the car from the base of the building?

Draw a diagram to help solve this problem:

Answer: _______ metres (to 2 decimal places)

10. Explain in your own words when you would use each trigonometric ratio (SOH-CAH-TOA):