Unit 3: Geometry and Trigonometry
Topic 3.2: Triangle Trigonometry Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026
A right-angled triangle has the side adjacent to angle θ equal to 9 and the opposite side equal to 5. Find θ to 3 s.f.
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2021
Write down the exact area of a triangle with sides and and an angle of between them.
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The two shorter sides of a right-angled triangle measure 6 cm and 8 cm. Work out the hypotenuse.
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2026
A triangle has sides 9 and 10 with an included angle of . Find its area, to 3 s.f.
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A metal plate is a triangle with two edges of 11 cm and 14 cm meeting at 38°. Work out its area, to 3 s.f.
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2026
A triangle has sides 12 cm and 15 cm enclosing an angle of 25°. Find its area, to 3 s.f.
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2026
An isosceles triangle has two sides of length 4 cm with an included angle θ.
Describe the effect on the shape of the triangle as θ approaches π.
Describe the effect on the shape of the triangle as θ approaches π.
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2026
A right-angled triangle has legs of 8 and 15. Find the hypotenuse.
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A ramp forms a right-angled triangle whose sloping edge is 18 cm long and which contains an angle of 27°. Calculate the horizontal side beside that angle, to 3 s.f.
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2026
A triangle has sides 12 cm and 15 cm enclosing an angle of . Find its area, to 3 s.f.
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2021
A triangle has two sides of length with an angle of between them. Write down its area in terms of and .
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2026
Write down an expression for the area of the triangle.
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2026
A rectangle is inscribed in a circle of radius r, with its diagonal making an angle θ with one side.
Describe the effect on the shape of the rectangle as θ approaches π/4.
Describe the effect on the shape of the rectangle as θ approaches π/4.
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2026
A straight ramp rises a height of metres over a horizontal distance of metres, and makes an angle with the horizontal. Show that .
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2022
In triangle , , and . Find an expression for in terms of .
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In a triangle you know two sides and the angle between them, and you need the third side. Choose the correct method.
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In a triangle containing a right angle, the side beside angle θ measures 11 cm and the side facing θ measures 7 cm. Determine θ, to 3 s.f.
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2026
A triangle has sides 9 and 10 with an included angle of 40°. Find its area, to 3 s.f.
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2026
A right-angled triangle has hypotenuse 20 and an angle of 35°. Find the length of the side opposite the 35° angle, to 3 s.f.
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