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Right Triangle Review: Pythagorean Theorem Concepts: Pythagorean Theorem: In a right triangle: βπ¦πππ‘πππ’π π 2 = πππ2 + πππ2 Classifying if three values make a triangle, and the type of triangle To test if a triangle: Sum of the two smaller numbers > the largest side To test the type of triangle ππππππ π‘ ππ’ππππ 2 = π ππππππ ππ’ππππ 2 + ππ‘βππ π ππππππ ππ’ππππ 2 ππππππ π‘ ππ’ππππ 2 > π ππππππ ππ’ππππ 2 + ππ‘βππ π ππππππ ππ’ππππ 2 ππππππ π‘ ππ’ππππ 2 < π ππππππ ππ’ππππ 2 + ππ‘βππ π ππππππ ππ’ππππ 2 Please note---must put largest number on the left right triangle obtuse triangle acute triangle Special Triangles: 45°-45°-90° legs are congruent Hypotenuse = leg β2 30°-60°-90° hypotenuse = 2short leg Long leg = short leg β3 remember the short leg is opposite the 30° angle remember the long leg is opposite the 60° angle Some problems are easy, some are tougherβit depends what number is given and which side it is Similar Right Triangles with altitude: (πππ‘ππ‘π’ππ)2 = (1st piece of hypotenuse) (other piece of hypotenuse) (πππ)2 = (entire hypotenuse) (adjacent piece of hypotenuse) Trigonometric Problems: SOH-CAH-TOA sinπ= πππππ ππ‘π πππ βπ¦πππ‘πππ’π π cosπ= ππππππππ‘ πππ βπ¦πππ‘πππ’π π πππππ ππ‘π πππ tanπ= ππππππππ‘ πππ Adjacent side is next to (touching) the reference angle (but not the hypotenuse) Opposite side is across from the reference angle Rememberβthere were three kinds of problems Writing ratios---which are fractions (no calculator needed) Finding a missing side (calculator) Finding a missing angle (calculatorβuse second key) Word Problems Angle of elevation = angle of depression Angle of elevationβis an angle looking up (inside the right triangle) Angle of depressionβis an angle looking down (it is not in the right triangle so you must move it to the angle of elevation)
