Unit 8 Right Triangles and Trigonometry – Flashcards
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Pythagorean Theorem
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If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
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Converse of the Pythagorean Theorem
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If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.
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If the square of the length of the longest side of a triangle is _______________the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.
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greater than
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If the square of the length of the longest side of a triangle is ____________ the sum of the squares of the lengths of the other two sides, then the triangle is acute.
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less than
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45-45-90 Triangle Theorem
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In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse is radical 2 times the length of a leg.
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30-60-90 Triangle Theorem
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In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is radical 3 times the length of the shorter leg.
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pythagorean triple
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a set of nonzero numbers a, b, and c that satisfy the equation a^2 + b^2 = c^2
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trigonometric ratios
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ratios of side lengths in a right triangle; sine, cosine, and tangent; SOHCAHTOA
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sine (sin)
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opposite/ hypotenuse
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Cosine (cos)
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adjacent/hypotenuse
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tangent (tan)
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opposite/adjacent
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angle of elevation
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an angle formed by a horizontal line and the line of sight to an object above the horizontal line
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angle of depression
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an angle formed by a horizontal line and the line of sight to an object below the horizontal line
