# Trigonometry

## 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.

 1 2 3 4 5 6 7 Calculate the size in degrees of angle QRP if:     PQ = 153 metres;     QR = 255 metres;     RP = 204 metres. angle QRP = ° 8 In triangle ABC the angle at B is 90°. If BC = 14mm and AB = 31mm find the size of the angle at C in degrees. angle C = ° 9 In triangle DEF the angle at E is 90°. If DF = 13m and the angle at F is 37° find the length of the side DE. DE = m 10 Calculate the length of the hypotenuse of this right-angled triangle if the length of the base (shown as d in the diagram) is 40 metres. = m 11 Miriam is lying on a flat, horizontal beach looking up at the top of a 41m high cliff which is 51m away. Find the angle of elevation of the top of the cliff from Miriam's position on the beach. angle = ° 12 The diagram shows an isosceles triangle. The equal angles, x, are each 73 degrees and the equal sides, f, are each 18 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 13 Find the smallest angle of an isosceles triangle that has one side of length 1.9cm and two sides of length 6.3cm.[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 = ° 14 Find m if n = 76cm, p = 41° and s = 27°. m = cm 15 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 = °
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This is Trigonometry level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 8

## Instructions

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## Transum.org

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Description of Levels

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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).

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## Curriculum Reference

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

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