A special right triangle is a right triangle whose sides are in a particular ratio, called the Pythagorean Triples. You can also use the Pythagorean theorem ', but if you can see that it is a special triangle it can save you some calculations. The following figures show some examples of special right triangles and Pythagorean Triples. Teaching the Unit Circle is hard enough if they haven't mastered the Special Right Triangles it becomes a nightmare! Special Right Triangles Worksheet and Guided Notes. Below are a Worksheet and Guided Notes to assist you in your lesson but one way I found very effective is to teach them a jingle to remember these few special triangles. Special Right Triangles Date Period Find the missing side lengths. Leave your answers as radicals in simplest form. 1) a 2 2 b 45° 2) 4 x y 45° 3) x y 3 2 2 45° 4) x y 3 2 45° 5) 6 x y 45° 6) 2 6 y x 45° 7) 16 x y 60° 8) u v 2 30°-1.

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. Right Triangles Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the length of the missing side. The triangle is not drawn to scale. Triangle ABC has side lengths 9, 40, and 41. Do the side lengths form a.

Special Right Triangles

Special Right Triangles 30 60 90

Key Questions

Special Right Triangles Examples

• Answer:

  Consider the properties of the sides, the angles and the symmetry.

  Explanation:

  #45-45-90' '# refers to the angles of the triangle.

  Lego batman 2 mac download. 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.')#

• #mathbf{30^circ'-'60^circ'-'90^circ}# Triangle

  The ratios of three sides of a #30^circ'-'60^circ'-'90^circ# triangle are:

  #1:sqrt{3}:2#

  I hope that this was helpful.

• 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.

• 1. #30^circ#-#60^circ#-#90^circ# Triangles whose sides have the ratio #1:sqrt{3}:2#

  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#.

Special Right Triangles Quizlet

Questions