Ontario · MPM2D · Grade 10
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.
What you need to know
- SOH CAH TOA — sin=opp/hyp, cos=adj/hyp, tan=opp/adj.
- Sine law — a/sinA=b/sinB, use when you have an angle-side pair.
- Cosine law — c²=a²+b²−2ab cosC, use for SAS or SSS.
- Bearings — start at north, turn clockwise; depression = alternate interior angle.
Practice Questions (4)
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 $$\sin \theta$$, $$\cos \theta$$, and $$\tan \theta$$.
Show Solution
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.
Show Solution
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.
Show Solution
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.
Show Solution
θ = tan⁻¹(0.8173)
θ ≈ 39.3°
Use the inverse tangent function on your calculator.
Answer: 39.3 degrees
Common mistakes
- Picking the wrong ratio — label opp/adj/hyp first.
- Calculator in radian mode.
- Mixing sine and cosine law — cosine needs the included angle.
- Rounding too early; keep one extra decimal.