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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
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
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)
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)
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)
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.
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
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