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Resources tagged with Mixed trig ratios similar to Cosines Rule:

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Broad Topics > Trigonometry > Mixed trig ratios

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Cosines Rule

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

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Circle Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?

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Round and Round

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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Trigonometric Protractor

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.

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Screen Shot

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

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History of Trigonometry - Part 3

Stage: 3, 4 and 5

The third of three articles on the History of Trigonometry.

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Circle Scaling

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.

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Coke Machine

Stage: 4 Challenge Level: Challenge Level:1

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly. . . .

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Raising the Roof

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How far should the roof overhang to shade windows from the mid-day sun?

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The History of Trigonometry- Part 1

Stage: 3, 4 and 5

The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.

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History of Trigonometry - Part 2

Stage: 3, 4 and 5

The second of three articles on the History of Trigonometry.

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Making Maths: Clinometer

Stage: 3 Challenge Level: Challenge Level:1

Make a clinometer and use it to help you estimate the heights of tall objects.

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Swings and Roundabouts

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If you were to set the X weight to 2 what do you think the angle might be?

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Circumnavigation

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

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At a Glance

Stage: 4 Challenge Level: Challenge Level:1

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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Farhan's Poor Square

Stage: 4 Challenge Level: Challenge Level:1

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

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Eight Ratios

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

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From All Corners

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Six Discs

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?