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Right Triangle/Trigonometry Geometric Means: means are the same. Multiply 2 numbers together and take square root of it. Remember 2 solutions: 1 positive and 1 negative. o When simplifying radicals, do not give decimals. Use simplifying methods discussed in class and found in notes. Application: Pythagorean Theorem o Most common triples 3-4-5 5-12-13 7-24-25 8-15-17 9-40-41 Special Right Triangles o 45-45-90: 2 legs have the same value and the hypotenuse is leg * sqrt of 2 o 30-60-90: hypotenuse is 2 * 30-leg and the 60-leg is 30-leg * sqrt of 3 Trig Ratios o SOH-CAH-TOA o Adjacent - leg next to specified angle o Opposite - leg across from specified angle Types of Triangles o a^2 + b^2 = c^2 right o a^2 + b^2 < c^2 obtuse o a^2 + b^2 > c^2 acute Hwk Hints o Simplify Radicals WS: #11 & 12: divide 1st and then simplify radicals #13: multiply both numerator and denominator by sqrt of 2 o Pythagorean Property WS Part I: Make sure to provide me with the simplified square root value Part II: make sure you select the largest number to be the c value and make the others the a & b. o Solve Right Triangle WS #4 & #5: use pythagorean theorem to find the missing side and then use the appropriate trig ratios to find the missing angles. o Law of Sines/Cosines WS #1 & 4: Use law of cosines 1st #2 & 3: Use law of sines o Angle of Depression/Elevation WS #5: use sin #3, 4, 6, 7: use tan Right Triangle/Trigonometry Quizzes/Exams Geometric Means/Pythagorean Theorem Quiz Hints o Be able to identify the legs and hypotenuse of a right triangle. o Be able to determine if 3 sides make up a right triangle. If not, what do they form? o Be able to find the missing side of a right triangle using Pythagorean theorem or geometric means (for altitude) o Honors/Magnet: Be able draw, set up and solve word problem using Pythagorean theorem. Right Triangle Quiz #2 Hints o Remember your Pythagorean triples o Know the relationships between the various sides/angles of the 30-60-90 and 45-45-90 triangles o Be able to identify the various trig ratios of a specified angle. o Be able to solve a right triangle. o At least 1 explanation question. o Remember, that the altitude of equilateral triangle is actually the 60-leg of 30-60-90 Right Triangle Quiz #3 Hints o Be able to solve a right triangle(all) and an oblique triangle (honors/magnet only) o Be able to solve for a specified angle/side of a right triangle using the appropriate trig ratio. Right Triangle/Trigonometry Exam (Honors/Magnet) Hints o Be able to solve a right and oblique triangles o Be able to identify the various trig ratios of a specified angle. o Be able to solve the ski problem (remember how much travel north/south is 1 leg, how much nd you travel east/west is 2 leg and distance travelled is the hypotenuse) o Be able to solve angle of elevation/depression problems o Know the Pythagorean triples. o Be able to find the length of a diagonal of a rectangle (Hint: use Pythagorean theorem) o Be able to find the perimeter of square/rhombus based on diagonals/sides and vice-versa o Be able to find the altitude of an equilateral triangle. o Be able to solve 45-45-90 and 30-60-90 triangles. o Be able to simplify a radical. o Be able to find the altitude or leg. o There will be a few real-world application problems similar to magnet’s trig on-line discussion.