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Last Week's Challenges
Last Week's Challenges
Week 7 - Challenge 1 Pt 1
Week 7 - Challenge 1 Pt 1
Week 7 - Challenge 1 Pt 2 Fail
Week 7 - Challenge 1 Pt 2 Fail
Week 7 - Challenge 1 Pt 2 Not a Fail
Week 7 - Challenge 1 Pt 2 Not a Fail
Week 7 - Challenge 2
Week 7 - Challenge 2
This week - Triangles
This week - Triangles
Triangles are really very useful, they have the fewest sides of any polygon, and all other shapes can be broken down into triangles (NB a circle contains infinitely many triangles.) This idea can lead to better approximations of pi and I seem to remember it being important somewhere in my maths degree. There are two really important concepts to do with triangles that you have already met. Pythagoras' Theorem and similarity/construction which leads to Trigonometry. So a few puzzles about triangles this week...
I would like to thank the wonderful people at underground maths. All of this weeks challenges have been adapted from their website.
Challenge 1 - What Type of Triangle?
Challenge 1 - What Type of Triangle?
For each set of points, determine what sort of triangle the three coordinates form (equilateral, isosceles, right-angled and scalene). How many of each type are there in the sets of coordinates given below?
(a) (9, −2), (4, 6), (20, 16).
(b) (3, 0), (−1, 0), (1, 21).
(c) (1, 1), (3, 2), (2, 4).
(d) (0, 3), (0, 15), (6√3, 9).
(e) (−2, −7), (1, −1), (5, 7).
(f) (2, −3), (−1, 1), (−4, 8).
Hint and Solution:
Hint and Solution:
How can you use Pythagoras' theorem to find distances between coordinates?
Challenge 2 - Trig Colouring
Challenge 2 - Trig Colouring
Take a look at this diagram
Take a look at this diagram
We’ve used inequalities involving sinθ, cosθ and tanθ to divide the semicircle into sectors.
We’ve used inequalities involving sinθ, cosθ and tanθ to divide the semicircle into sectors.
Each sector in the diagram is defined by a different inequality.
Each sector in the diagram is defined by a different inequality.
For example, one sector is defined by the angles θ between 0 and 180o for which cosθ<sinθ<tanθ.
For example, one sector is defined by the angles θ between 0 and 180o for which cosθ<sinθ<tanθ.
Another sector is defined by cosθ<tanθ<sinθ.
Another sector is defined by cosθ<tanθ<sinθ.
1) Can you work out which inequality has been used to define each sector
1) Can you work out which inequality has been used to define each sector
2) Which is the biggest sector?
2) Which is the biggest sector?
(Solution next week)
Challenge 4 - Inscribing a circle?
Challenge 4 - Inscribing a circle?
Can you accurately construct the inscribed circle of radius 6 inside a right angled triangle? If so, is the triangle unique?
Hint/Solution
Hint/Solution
Draw in radii to important points.
What are the sides of the triangle in relation to the circle?
This Week's Test and Last Week's Solutions
This Week's Test and Last Week's Solutions
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