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Sine, cosine and tangent ratios are used to find sides and angles in right-angled triangles.

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This is level 7: mixed questions (15 questions). You will be awarded a trophy if you get at least 10 correct and you do this activity online.  Give your answers correct to three significant figures. For the first six questions find the value of \(x\). Diagrams are not to scale.


Correct Wrong


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Calculate the size in degrees of angle QRP if:

    PQ = 222 metres;
    QR = 370 metres;
    RP = 296 metres.

angle QRP = ° Correct Wrong


In triangle ABC the angle at B is 90°. If BC = 26mm and AB = 36mm find the size of the angle at C in degrees.

angle C = ° Correct Wrong


In triangle DEF the angle at E is 90°. If DF = 24m and the angle at F is 45° find the length of the side DE.

DE = m Correct Wrong


Calculate the length of the hypotenuse of this right-angled triangle if the length of the base (shown as d in the diagram) is 27 metres.

= m Correct Wrong


Miriam is lying on a flat, horizontal beach looking up at the top of a 32m high cliff which is 36m away. Find the angle of elevation of the top of the cliff from Miriam's position on the beach.

angle = ° Correct Wrong


The diagram shows an isosceles triangle. The equal angles, x, are each 79 degrees and the equal sides, f, are each 87 metres.
Find the length of the shorter side of the triangle marked as d.

[Hint: Sketch a horizontal line on the diagram to split the isosceles triangle into two right-angled triangles.]

d = m Correct Wrong


Find the smallest angle of an isosceles triangle that has one side of length 4.2cm and two sides of length 7.4cm.

[Hint: Draw a sketch of the isosceles triangle then sketch its line of symmetry to split the isosceles triangle into two right-angled triangles.]

angle = ° Correct Wrong


DiagramFind m if n = 49cm, p = 40° and s = 22°.

m = cm Correct Wrong


In triangle PQR there is a right-angle at Q. The side PQ is twice as long as side QR. Calculate the size of angle RPQ.

angle RPQ = ° Correct Wrong


This is Trigonometry level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 8


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When planning to use technology in your lesson always have a plan B!

Joseph, Pleasanton

Tuesday, February 28, 2023

"It asked for the acute angle of diagonals in a rectangle with side lengths 3 and 9, so I typed in the answer to arctan(3/9) which is 18.4, but it kept saying I was wrong. Please help!

[Transum: Hi Joseph, I think you have found the angle between a diagonal and one of the sides of the rectangle. Read the question again carefully as that is not what is required.]"

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Description of Levels



Which Side? - Learn the names of the sides of a right-angled triangle before beginning trigonometry.

Level 1 - Using the sine ratio to find a side (10 questions)

Level 2 - Using the cosine ratio to find a side (10 questions)

Level 3 - Using the tangent ratio to find a side (10 questions)

Level 4 - Using the sine ratio to find an angle (10 questions)

Level 5 - Using the cosine ratio to find an angle (10 questions)

Level 6 - Using the tangent ratio to find an angle (10 questions)

Level 7 - Mixed questions (15 questions)

Level 8 - Review exercise (20 questions)

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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