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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 4, Mixed Questions. All lengths are in centimetres unless stated otherwise. Give all answers to three significant figures. The diagrams are not drawn to scale.

Find the size of the lettered sides and angles.

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cm Correct Wrong

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° Correct Wrong

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° Correct Wrong

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° Correct Wrong

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cm Correct Wrong

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cm Correct Wrong

A UFO is spotted in the sky. It begins by flying for \(10.5 \, \text{km}\) on a bearing of \(235^\circ\). It then changes direction and flies for another \(15.2 \, \text{km}\) on a bearing of \(130^\circ\). Find the bearing of the final position from the starting point.

° Correct Wrong

Find the area of an equilateral triangle with sides of length 3.14cm.

cm² Correct Wrong

Find the area of a regular pentagon with sides of length 75mm.

mm² Correct Wrong

Marty is making a map of his local area. He marks his house with the letter \(H\). He knows that his school is 2km from his house and he marks this with the letter \(S\). The park (\(P\)) is \(1.7km\) from school. Marty has found out that the angle \(P\hat{H}S \) is \(25^\circ \). What is the difference between the two possible values that angle \(S\hat{P}H\) could be?

° 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?

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"Really good site. Lots of good ideas for starters. Use it most of the time in KS3."

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"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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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Tran Towers

Tran Towers

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