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Posts tagged with trigonometry

Measuring the Roof of the World

April15

The history of measuring the tallest mountain in the world stretches back to 1852. In Europe, Charles Dickens was publishing serialised instalments of his novel Bleak House. North America had started testing its first steam-powered fire engine. In Asia, the height of Mount Everest was a mystery. It is known only as “Peak XV”. Radhanath […]

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An ancient tablet that demonstrates undoubted genius

August25

For nearly 100 years, the mysterious tablet above (no, it’s not an iPad) has been referred to as Plimpton 322. It was first discovered in Iraq in the early 1900s by Edgar Banks, the American archaeologist on which the character Indiana Jones is thought to have been largely based. Now researchers from the University of […]

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Trig Ratios Unplugged

May31

Sine, Cosine and Tangent are the three main trigonometric or Trig Ratios. Before we look at these in more detail, where did these strange terms come from? Trigonometric functions were studied by Hipparchus of Nicaea (180–125 BC), Ptolemy of Egypt (90–165 AD), Aryabhata (476–550), Varahamihira, Brahmagupta, Ulugh Beg and others (14th century). The word “sine” […]

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Sine Method used to measure tallest tree

January23

Scientists recently measured the tallest tree in New Zealand at just over 81 metres. How did they do this? Using lasers and the Sine method – that is, the Sine of the angle formed by the lasers gave the height/hypotenuse. Read more here. (Note: This image is not of the tallest tree but gives some […]

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The Art of Rectangular Pyramids

January15

Ah…The Louvre – perhaps the world’s most famous museum and an iconic, classical building which is noted for its modernistic entry which uses pyramids to contrast its surroundings. (H3 was taken aback by the beauty of this entry and the way in which it differed so much to the style of the French buildings and […]

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Angles of Depression and Elevation

September13

Angles of Depression and Angles of Elevation both relate to the view from a horizontal line. When someone is depressed they tend to look down and the same is true for an angle of depression – it is an angle looking down from an imaginary horizontal line. In the sketch below, imagine someone in the […]

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Touch Mathematics – cool curves

November2

Click here for the simpler Unit Circle of Sine

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Go West Young Man!

May31

Yes, the cry of the early USA settlers was “Go West Young Man”. This exciting period of exploration led to large numbers of people travelling out to Oregon in the far west (read some interesting Trail Facts here). They faced incredible difficulties and many challenges, not only on the journey but also in settling into […]

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Post Support

Largest number between o and 1 million which does not contain the ‘n’ is 88

 

Rotation SAT Problem: Answer: 4 (see: https://www.youtube.com/watch?v=FUHkTs-Ipfg)

 

Which number has its letters in alphabetical order? Answer: F O R T Y

Hidden Rabbit? Clue: check the trees

How long for the stadium to fill? 45 minutes.

Where are you? the North Pole

Prize Object Puzzle: If Sue does not know where the prize is in the first question, it can’t be under the square. She must have been told it is under another shape. Apply this same logic to Colin. It is then obvious that the prize cannot be under a yellow object. That helps Sue eliminate her yellow shapes. Got the idea?

Algebra Puzzle: Answer = 1

Popular Math Problems Answers: 1, 1

Number of tabs? According to Lifehacker, the ideal number of tabs you should have open is nine. Yes, a single digit. To some, this is like playing a piano and only using a fraction of the notes!

Worst Graph? Where to start. What a visual mess and even some of the lines merge and are impossible to follow. A graph is a visual display of data, with the goal to identify trends or patterns. This is a spider’s web of information which fails to show a clear pattern at all. Solution? Well, different colors would help, or why not group in two or three graphs where trends are similar?

Number of different nets to make a cube is eleven – see this link

Homework Puzzle; The total value of the counters is 486, so halve this to get 243. Now, arrange the counters to equal this amount twice.

The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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