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SOH-CAH-TOA Triangle Problems
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SOH-CAH-TOA Triangle Problems
Use a calculator in degree mode. Give side lengths to 2 decimal places and angles to 1 decimal place unless a question says otherwise.
Choose a ratio
For each question, identify the trigonometric ratio or inverse ratio that fits the information.
1.A right-angled triangle has θ = 30°, an opposite side of 4 cm and a hypotenuse of 8 cm. Which ratio checks the relationship between these sides?
- Sine
- Cosine
- Tangent
- None of these
2.You know the opposite and adjacent side lengths and need to calculate an acute angle. Which inverse ratio should you use?
- sin⁻¹
- cos⁻¹
- tan⁻¹
- No inverse ratio is needed
3.Which option correctly gives the cosine ratio?
- sin θ = opposite ÷ hypotenuse
- cos θ = opposite ÷ adjacent
- cos θ = adjacent ÷ hypotenuse
- tan θ = opposite ÷ adjacent
- tan θ = adjacent ÷ hypotenuse
Find a missing side
Write the ratio you use, then calculate the missing length.
4.In a right-angled triangle, θ = 45° and the hypotenuse is 14 cm. Calculate the side opposite θ.
5.Finn rests a 9 m ladder against a lighthouse wall. The ladder makes an angle of 62° with the level ground. How high up the wall does it reach?
6.In a right-angled triangle, the side adjacent to θ is 12 cm and θ = 38°. Find the opposite side.
7.A triangular support has a 5.5 m hypotenuse and an angle of 27° between the hypotenuse and the horizontal base. Calculate the length of the base.
Find a missing angle
Choose the inverse ratio that matches the known sides.
8.In a right-angled triangle, the opposite side is 6 cm and the hypotenuse is 13 cm. Find θ to 1 decimal place.
9.A straight access ramp rises 2.8 m over a horizontal distance of 16 m. What angle does the ramp make with the horizontal? Give your answer to 1 decimal place.
10.From a viewing platform 42 m above sea level, Mere measures a 31° angle of depression to a boat. Assuming level water, how far is the boat horizontally from the point directly below the platform? Give your answer to 2 decimal places.
11.In your own words, explain what information tells you to use sine, cosine or tangent when finding a side in a right-angled triangle.
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