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#### Resources tagged with Mixed trig ratios similar to Gold Again:

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Broad Topics > Trigonometry > Mixed trig ratios

### Gold Again

##### Stage: 5 Challenge Level:

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.

### At a Glance

##### Stage: 4 Challenge Level:

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

### Farhan's Poor Square

##### Stage: 4 Challenge Level:

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

##### Stage: 4 Challenge Level:

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

### Trigonometric Protractor

##### Stage: 4 Challenge Level:

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

### History of Trigonometry - Part 2

##### Stage: 3, 4 and 5

The second of three articles on the History of Trigonometry.

### 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.

### From All Corners

##### Stage: 4 Challenge Level:

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.

### History of Trigonometry - Part 3

##### Stage: 3, 4 and 5

The third of three articles on the History of Trigonometry.

### Six Discs

##### Stage: 4 Challenge Level:

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?

### Raising the Roof

##### Stage: 4 Challenge Level:

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

### So Big

##### Stage: 5 Challenge Level:

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

### Orbiting Billiard Balls

##### Stage: 4 Challenge Level:

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

### Screen Shot

##### Stage: 4 Challenge Level:

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. . . .

### Eight Ratios

##### Stage: 4 Challenge Level:

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.

### Cosines Rule

##### Stage: 4 Challenge Level:

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.

### Bend

##### Stage: 5 Challenge Level:

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

### 30-60-90 Polypuzzle

##### Stage: 5 Challenge Level:

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

### Circle Box

##### Stage: 4 Challenge Level:

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?

### Spokes

##### Stage: 5 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

### Coke Machine

##### Stage: 4 Challenge Level:

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

##### Stage: 4 Challenge Level:

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

### Round and Round

##### Stage: 4 Challenge Level:

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

### Circle Scaling

##### Stage: 4 Challenge Level:

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.

### Flight Path

##### Stage: 5 Challenge Level:

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.