Right Triangle/Trigonometry
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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
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7-24-25
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8-15-17
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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 pg 345 (regular):
 #16: sqrt of 38416 = 196
 #18: numerator becomes sqrt of (8 * 6 * 3) and denominator becomes sqrt of (5*5).
Simplify from there
 #28: to solve for x: 8 = sqrt(6(x-6)). Once you have x, you can find y and z
 #30: solve for z 1st, then the other variables. Hint: 10 = sqrt of (4(4+y))
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 pg360 (regular)
 #15: Need to figure out the value of the 30-leg before you can figure out the y and x.
Hint: 30-leg *sqrt3 = 12; 30-leg = 4 sqrt 3
o Solve Right Triangle WS
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#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
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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.
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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.
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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.
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Right Triangle/Trigonometry Exam (Regular) Hints
o Be able to solve a right triangle
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
you travel east/west is 2nd leg and distance travelled is the hypotenuse)
o Be able to solve angle of elevation/depression problems
o Be able to find the trig value of any angle using a calculator
o Be able to find the angle based on a trig value using a calculator (remember to use inverse
trig function here)
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 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.
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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
you travel east/west is 2nd 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.