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Advanced Trigonometry

A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle.

Sine Rule Cosine Rule Sine Formula Mixed Questions Exam Help More

This is level 3, Sine Formula. All lengths are in centimetres unless stated otherwise. Give all answers to three significant figures. The diagrams are not drawn to scale.

Find the areas of these triangles.

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cm² Correct Wrong

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cm² Correct Wrong

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cm² Correct Wrong

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cm² Correct Wrong

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cm² Correct Wrong

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cm² Correct Wrong

Find the area of triangle ABC if AB = 17.7cm, BC = 26.3cm, angle BCA = 62° and angle CAB = 53°.

cm² Correct Wrong

Find the area of triangle ABC if AB = 17.7cm, BC = 26.3cm and AC = 18.6cm.

cm² Correct Wrong

In the triangle ABC find the length of AB if, BC = 26.3cm, angle ABC = 44° and the area of the triangle is 186cm²

cm Correct Wrong

Find the area of a triangular shaped park if its vertices are at X, Y and Z where Y is due east of X, Z is on a bearing of 048° from X and the lengths of XY and XZ are both 3km.

km² Correct Wrong

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Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Whose Idea Was This?

Did you enjoy doing this 'Advanced Trigonometry' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

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23 or Bust

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Answers

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Teachers

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