Special Right Triangles
Key Questions
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Answer:
Consider the properties of the sides, the angles and the symmetry.
Explanation:
#45-45-90" "# refers to the angles of the triangle.The
#color(blue)("sum of the angles is " 180°)# There are
#color(blue)("two equal angles")# , so this is an isosceles triangle.It therefore also has
#color(blue)(" two equal sides.")# The third angle is
#90°# . It is a#color(blue)("right-angled triangle")# therefore Pythagoras' Theorem can be used.The
#color(blue)("sides are in the ratio " 1 :1: sqrt2)# It has
#color(blue)("one line of symmetry")# - the perpendicular bisector of the base (the hypotenuse) passes through the vertex, (the#90°# angle).It has
#color(blue)("no rotational symmetry.")# 
EZ as pi
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Apr 21 2018
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#mathbf{30^circ"-"60^circ"-"90^circ}# TriangleThe ratios of three sides of a
#30^circ"-"60^circ"-"90^circ# triangle are:#1:sqrt{3}:2#
I hope that this was helpful.
Wataru
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1
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Nov 6 2014
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Each black-and-red (or black-and-yellow) triangles is a special right-angled triangle. The figures outside the circle -
#pi/6, pi/4, pi/3# - are the angles that the triangles make with the horizontal (x) axis. The other figures -#1/2, sqrt(2)/2, sqrt(3)/2# - are the distances along the axes - and the answers to#sin(x)# (yellow) and#cos(x)# (red) for each angle.CJ · 5 · Dec 13 2014
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#30^circ# -#60^circ# -#90^circ# Triangles whose sides have the ratio#1:sqrt{3}:2# -
#45^circ# -#45^circ# -#90^circ# Triangles whose sides have the ratio#1:1:sqrt{2}#
These are useful since they allow us to find the values of trigonometric functions of multiples of
#30^circ# and#45^circ# .
Wataru
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Dec 7 2014
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