Ontario Grade 10 Math

Unit 6 · Ontario MPM2D

Ontario Grade 10 Trigonometry Practice Questions

Ratios on triangles. SOH CAH TOA on right triangles; sine and cosine laws when there's no right angle. Draw the triangle, label what you know, pick the tool. Keep your calculator in degrees.

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Practice questions with solutions

4 questions. Try each one on paper, then open the worked solution.

Question 1 · More Primary Trig Ratios

In a right triangle with angle θ, the opposite side is 5, the adjacent side is 12, and the hypotenuse is 13. Find sin⁡θ\sin \theta, cos⁡θ\cos \theta, and tan⁡θ\tan \theta.
θ 12 5 13
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sin θ = opposite/hypotenuse = 5/13 cos θ = adjacent/hypotenuse = 12/13 tan θ = opposite/adjacent = 5/12.

Answer: sin=5/13, cos=12/13, tan=5/12

Question 2 · Primary Trig Ratios

In a right triangle with angle θ, the opposite side is 3, the adjacent side is 4, and the hypotenuse is 5. Find sin θ, cos θ, and tan θ.
3 4 5 θ
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sin θ = opposite/hypotenuse = 3/5 cos θ = adjacent/hypotenuse = 4/5 tan θ = opposite/adjacent = 3/4 This is the classic 3-4-5 right triangle!

Answer: sin=3/5, cos=4/5, tan=3/4

Question 3 · Primary Trig Ratios

In a right triangle with angle θ, the opposite side is 6, the adjacent side is 8, and the hypotenuse is 10. Find sin θ, cos θ, and tan θ as decimals rounded to 2 decimal places.
6 8 10 θ
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sin θ = 6/10 = 0.60 cos θ = 8/10 = 0.80 tan θ = 6/8 = 0.75 This is a 6-8-10 triangle (scaled 3-4-5).

Answer: sin=0.60, cos=0.80, tan=0.75

Question 4 · Primary Trig Ratios

Find the measure of angle θ to the nearest tenth of a degree if tan θ = 0.8173.
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θ = tan⁻¹(0.8173) θ ≈ 39.3° Use the inverse tangent function on your calculator.

Answer: 39.3 degrees

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