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15 terms

Flashcards for McDougal Littell Geometry Chapter 7 Right Triangles

Pythagorean Theorem

In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2

Obtuse triangle

In a triangle with shorter sides a and b and longer side c, if a^2 + b^2 < c^2, then the triangle is obtuse

Acute triangle

In a triangle with shorter sides a and b and longer side c, if a^2 + b^2 > c^2, then the triangle is acute

Pythagorean Triple

Three positive integers that satisfy a^2 + b^2 = c^2, that is, they could be the three side lengths of a right triangle. Primitive triples include: 3, 4, 5; 5, 12, 13, and 8, 15, 17. More triples can be formed by multiplying each member of a primitive triple by the same multiplier; for example, since 3, 4, 5 is a triple, so is 6, 8, 10.

45-45-90 right triangle

Special right triangle: isosceles right triangle where the legs are congruent and the hypotenuse = leg * sqrt(2)

30-60-90 right triangle

Special right triangle: hypotenuse = shorter side ** 2; longer side = shorter side ** sqrt(3)

sine

trigonometric ratio: abbreviation sin; the sine of an acute angle in a right triangle equals the side opposite the angle divided by the hypotenuse (sin A = opp/hyp)

cosine

trigonometric ratio: abbreviation cos; the cosine of an acute angle in a right triangle equals the side adjacent to the angle divided by the hypotenuse (cos A = adj/hyp)

tangent

trigonometric ratio: abbreviation tan; the tangent of an acute angle in a right triangle equals the side opposite the angle divided by the adjacent side (tan A = opp/adj)

SOH CAH TOA

Mnemonic device to help remember the trig ratios in a right triangle: sin = opp/hyp; cos = adj/hyp; tan = opp/adj

Inverse Trig Ratio

Gives us the measure of the angle whose sin/cos/tan is a given ratio value. "Undoes" sin, cos, or tan. Written using a "-1" (looks like an exponent, but isn't). Also called "arc," such as arcsin, arccos, arctan. Example: arcsin(1/2) = 30 degrees. Useful in finding missing angle values in right triangles.

trigonometric ratios

Ratios formed by the sides of a right triangle. Useful in finding the missing sides of a right triangle given an angle and a side. Trigonometric ratios include sine (sin), cosine (cos), and tangent (tan). Other ratios (not covered in this chapter) are: cosecant, secant, and cotangent

Solve a triangle

Means finding any missing angles and/or sides in a triangle. Methods to solve a right triangle include the Pythagorean theorem, triangle sum theorem (if given one acute angle in a right triangle, we can find the other by subtracting the acute angle's measure from 90), trig ratios, and inverse trig functions

Angle of elevation

The angle formed when looking up from the horizontal

Angle of depression

The angle formed when looking down from the horizontal