Right Triangles

RIGHT TRIANGLE: a triangle (plane figure having three sides and three angles) with one of the angles being a right angle (one angle = 90 degrees = 90^O). Probably one of the most studied and used types of all triangles.

Right triangles are the historic basis from which the field of trigonometry evolved. Trigonometry basically began with a recognition that the sides and angles in a right triangle had linkage. Ratios (division relationships) of lengths of sides in a right triangle were linked to the actual measures of the acute angles in the triangle.

Great Colby Indian Chief:  SOH-CAH-TOA

Sine Angle = (Opposite leg) / (Hypotenuse) ... sin A = a / c

Cosine Angle = (Adjacent leg) / (Hypotenuse) ... cos A = b / c

Tangent Angle = (Opposite leg) / (Adjacent leg) ... tan A = a / b

Two special right triangles:

30-60-90 with side ratios of 1 to sqrt(3) to 2
(hypotenuse is twice the shorter leg)

45-45-90 isosceles right triangle with side ratios of 1 to 1 to sqrt(2)
(hypotenuse is the square root of 2 times either of the equal legs)