Review Sheet Chapter Eight Pythagorean Theorem a 2

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Review Sheet Chapter Eight Pythagorean Theorem: a 2 +b 2 = c 2 where

Review Sheet Chapter Eight Pythagorean Theorem: a 2 +b 2 = c 2 where c is the longest side (hypotenuse) in the right triangle Common Pythagorean Triples: 3 – 4 – 5; 5 – 12 – 13; 8 – 15 – 17 and their multiples Triangle Trigonometry: Formulas are now on the formula sheet, but knowing them still helps Draw picture of triangle described in a word problem to help out with setting up proper trig function • 1. Label each side of the triangle as H for hypotenuse (opposite 90°) O for opposite the given angle A for side adjacent to given angle Set up an equation using the trig function and the variable Angle of Elevation or Angle of Depression H O Some Side Trig Fnc (angle) = ------------Some other Side angle A SOH – CAH – TOA: Sin (angle) = side opposite from the angle / hypotenuse Cos (angle) = side adjacent to the angle / hypotenuse Tan (angle) = side opposite from the angle / side adjacent to the angle • Solve for the variable All triangular trig problems are solved in one of three ways: Special Case Right Triangles Angle Side Opposite Variable Calculator Eqn 30 ½ hyp Top X = bottom Trig Fnc (angle) 45 ½ hyp √ 2 Bottom X = top / Trig Fnc (angle) 60 ½ hyp √ 3 Angle X = Trig Fnc-1 (top/bottom) Test Taking Tips: Remember virtual alligator when comparing sides and their opposite angles (big side opposite big ) Tan 45° = 1; bigger the angle the larger the sine and the smaller the angle the larger the cosine

Sin and cos are always between 0 and 1; so first statement is false.

Sin and cos are always between 0 and 1; so first statement is false. Sin CAB and cos CBA are always equal since the opposite side of CAB is the adjacent side of cos CBA CAB DAB only if ACBD is a square (y = x) Pythagorean theorem is true!! AD // CB because ACBD is a parallelogram

A ladder leans against a wall. The bottom of the ladder is 10 feet

A ladder leans against a wall. The bottom of the ladder is 10 feet from the base of the wall, and the top of the ladder makes an angle of 25° with the wall. Find the length, x, of the ladder.

SSM: • AC must be greater than 4, but less than 8 (since any

SSM: • AC must be greater than 4, but less than 8 (since any two sides must be greater than the third in a triangle). half of AC = 4 / sin 60° = 2 3

Coordinate Relations and Transformations Ch 8 SSM: • x is opposite larger angle •

Coordinate Relations and Transformations Ch 8 SSM: • x is opposite larger angle • eliminate A and B X is the adjacent side of the 20 angle. Use trig: cos 22 = x/80 80 cos 20 = x 75. 17 = x

Coordinate Relations and Transformations Ch 8 SSM: • right triangle Pythagorean theorem (on formula

Coordinate Relations and Transformations Ch 8 SSM: • right triangle Pythagorean theorem (on formula sheet) Have to use each set of numbers in the Pythagorean theorem to see which works 202 + 212 = 292 400 + 441 = 841

Ch 8 Coordinate Relations and Transformations SSM: • height is smaller than 14 •

Ch 8 Coordinate Relations and Transformations SSM: • height is smaller than 14 • eliminate A and B Special case right triangles; side opposite 60 = ½ hypotenuse 3 hypotenuse = 14, so answer is ½(14) 3 = 7 3

Coordinate Relations and Transformations Ch 8 SSM: • hypotenuse is largest side • length

Coordinate Relations and Transformations Ch 8 SSM: • hypotenuse is largest side • length > 20 • Eliminate A and B 20 foot side is opposite of the 38 angle, so we can us sine sin 38 = 20 / hyp sin 38 = 20 hyp = 20 / sin 38 hyp = 32. 49

Triangles Ch 8 SSM: • draw figure • diagonals bigger than the sides Diagonals

Triangles Ch 8 SSM: • draw figure • diagonals bigger than the sides Diagonals of a square form a 45 -45 -90 degree triangle. Sides opposite a 45 angle is ½ hypotenuse 2. Diagonal is the hypotenuse so side is ½ (14) 2 = 7 2

Triangles Ch 8 SSM: • Virtual Alligator • x across from bigger side so

Triangles Ch 8 SSM: • Virtual Alligator • x across from bigger side so eliminate A and B No hypotenuse, so we must use tangent. tan x = 8/7. 8 x = tan-1 (8/7. 8) = 45. 7

Triangles Ch 8 20 cm 21 cm 29 cm SSM: • hypotenuse is largest

Triangles Ch 8 20 cm 21 cm 29 cm SSM: • hypotenuse is largest side so either 21 or 29 Use the Pythagorean Theorem and the numbers to pick out which work. 202 + 212 = 292 400 + 441 = 841

Triangles Ch 8 SSM: • across from smallest angle, so small side (eliminate A

Triangles Ch 8 SSM: • across from smallest angle, so small side (eliminate A and B) x is opposite side from angle in right triangle. We use trig to find the answer. sin 22 = x/15 15 sin 22 = x 5. 62=x