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# Chapter 7 Notecards

TermDefinition
Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs
Pythagorean Triple a set of three positive integers a, b, and c that satisfy the equation c2 = a2 + b2. The most common ones are: (3,4,5), (5,12,13), (8,15,17), (7,24,25)
Converse of Pythagorean Theorem if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
Theorem 7.3 if the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides then the triangle is an acute triangle
Theorem 7.4 if the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle
Theorem 7.5 if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other
Geometric Mean (Altitude) Theorem In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments.
Geometric Mean (Leg) Theorem the altitude from the right angle to the hypotenuse divides the hypotenuse into 2 segments. The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
45-45-90 Theorem The hypotenuse is square root 2 times as long as each leg
30-60-90 Theorem the hypotenuse is twice as long as the shorter leg, and the longer leg is square root 3 times as long as the shorter leg
Trigonometric Theorem a ratio of the lengths of two sides in a right triangle.
Tangent The ratio of the lengths of the legs in a right triangle is constant for a given angle measure
Tangent Ratio a trigonometric ratio, abbreviated as tan, for a right triangle ABC the tangent of <A (written as tan A) is defined as: tan A= length of leg opposite <A / length of leg adjacent to <A
Sine A trigonometric ratio, abbreviated as sin.
Cosine A trigonometric ratio, abbreviated as cos. For a right triangle
Sine Ratio Let triangle ABC be a right triangle w/ acute <A... sin A = length of leg opposite <A / length of hypotenuse
Cosine Ratio Let triangle ABC be a right triangle w/ acute <A... cos A = length of leg adjacent to <A / length of hypotenuse
Angle of Elevation if you look up at an object, the angle your line of sight makes with a horizontal line.
Angle of Depression If you look down at an object, the angle you line of sight makes with a horizontal line
Solve a Right Triangle means to find the measures of all of its sides and angles if you have either two side lengths or one side length and the measure of one acute angle.
Inverse Tangent Ratio if tan A = x, then tan-1x = m<A
Inverse Sine Ratio if sin A= y, then sin-1y = m<A
Inverse Cosine Ratio if cos A= z, then cos-1z = m<A