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SOH-CAH-TOA Practice Worksheet
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SOH-CAH-TOA Practice Worksheet
Use SOH-CAH-TOA to solve each right-angled triangle problem. Label sides opposite, adjacent and hypotenuse relative to the marked angle θ. Give angles to 1 decimal place and lengths to 2 decimal places unless told otherwise. Use a calculator in degree mode.
Quick ratio check
Remember: sin θ = opposite ÷ hypotenuse; cos θ = adjacent ÷ hypotenuse; tan θ = opposite ÷ adjacent.
1.A rescue drone measures a right-angled triangle with opposite side 9 m and hypotenuse 15 m. What is sin θ? Choose the simplest fraction.
- 3/5
- 5/3
- 9/6
- 4/5
2.A triangular trail sign has adjacent side 7 cm and hypotenuse 25 cm at angle θ. Complete: cos θ = ÷ = .
3.A path rises 5 m for every 12 m horizontally. Which trigonometric ratio links the angle of elevation θ to these two lengths?
- Sine
- Cosine
- Tangent
Angles and distances on the route
Sketches are not to scale. Use inverse trigonometric functions when finding an angle.
4.At a lookout point, a right triangle has opposite side 6 m and adjacent side 8 m relative to θ. Find θ to 1 decimal place. Show the ratio and inverse operation.
5.A survey triangle has hypotenuse 13 cm and opposite side 5 cm to θ. Calculate θ to 1 decimal place. State which ratio you use.
6.A 10 m safety rope runs from the ground to a platform, making an angle of 60° with the horizontal ground. How high is the platform? Give your answer to 2 decimal places.
7.A cliff-top platform is 18 m above sea level. A boat is sighted at an angle of depression of 30°. Assuming level sea, how far is the boat horizontally from the cliff base? Give your answer to 2 decimal places.
8.A right-angled survey triangle ABC has angle C = 90°, AB = 15 cm and angle A = 40°. Find BC, to 2 decimal places. Show the trigonometric equation.
9.A mapmaker finds tan θ = 1. What is θ in a right-angled triangle? Explain briefly why this makes sense.
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