Geometry Chapter 7 Right Triangles Flashcards
5 Written Questions
5 Multiple Choice Questions
- 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
- 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)
- 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
- Special right triangle: hypotenuse = shorter side 2; longer side = shorter side sqrt(3)
- The angle formed when looking up from the horizontal
5 True/False Questions
Pythagorean Triple → In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2
trigonometric ratios → 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.
Solve a 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
SOH CAH TOA → Mnemonic device to help remember the trig ratios in a right triangle: sin = opp/hyp; cos = adj/hyp; tan = opp/adj
Pythagorean Theorem → 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.