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Preview and Download !The Pythagorean Theorem and Its Converse Date_____ Period____ Find the missing side of each triangle. Round your answers to the nearest tenth if necessary. 1) x 12 in 13 in 5 in 2) 3 mi 4 mi x 5 mi 3) 11.9 km x 14.7 km 8.6 km 4) 6.3 mi x 15.4 mi 14.1 mi Find the missing side of each triangle. Leave your answers in simplest radical form. 5) x
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Preview and Download !Instruction Exploring the Pythagorean Theorem Pythagorean Triples A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem and are possible lengths of a right triangle. • Side lengths 3, 4, and is a Pythagorean triple because 32 + 42 = 52. • (5, 12, 13) 52 + = 132 25 + 144 = 169 169 = 169ü • (7, 24, 25) 72 + 242 =
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Preview and Download !3 tan 2 Example 1: Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. a.tan𝜃cos𝜃 b.1−cos 2𝜃 cos2𝜃 c.cos𝜃csc𝜃 d.sin𝜃sec𝜃 tan𝜃 Example 2: Simplify the complex fraction. a. 2 3 4 15 b. 4 5 4 35 c. 2 5 3 5 d. 1 2 2 sin𝜃= 1 csc𝜃 csc𝜃= 1 sin𝜃
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Preview and Download !Converse of the Pythagorean TheoremIf the sum of the squares of the measures of the two shorter sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. If the three whole numbers a, b, and c satisfy the equation a2 2b c2, then the numbers a, b, and c form a If a2 b2 c2, then Pythagorean ...
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Preview and Download !Pythagorean triples are connected to points on the unit circle: if a2 + b2 = c2 then (a=c)2 + (b=c)2 = 1. So we get a rational point (a=c;b=c) on the unit circle x2 + y2 = 1. For a primitive Pythagorean triple (a;b;c), the rst paragraph of the previous proof shows we can take aodd and beven. Having done that, draw the line through ( 1;0) and
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Preview and Download !Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth. Answer Key Pythagorean Theorem Sheet 1 Printable Worksheets @ www.mathworksheets4kids.com Name : 4) XZ = 5) EF = 6) JL = 14 in? 3 in Z Y X t? 8 ft F G E 17 yd? 13 yd K L J 205 » 14.3 in 6 ft 458 » 21.4 yd 1) BC = 2) PQ = 3 ...
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Preview and Download !integers a Pythagorean triple (or just a triple, for short). People often list the integers of a triple inside parentheses, like “( , , ).” For example, in addition to the Pythagorean triple (3,4,5) mentioned above, a few other triples are (6,8,10), (5,12,13), and (8,15,17) because, as you can verify, 62 +82 = 102, 52 +122 = 132, 82 +152 ...
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Preview and Download !Pythagorean Theorem Worksheets Created Date: 1/27/2022 11:49:10 AM ...
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Preview and Download !Pythagorean Theorem in 3-D Shapes Name: _____ Date: _____ Directions: Use the Pythagorean Theorem to find the missing length in the three-dimensional shape. 1. A 45 meter rope is attached inside an empty cylindrical wheat silo of diameter 27 meters. How high is the wheat silo? 2. The floor of a room is 6 m by 4 m and its height is ...
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