Geometry Chapter 7 Right Triangles Flashcards

5 Written Questions

1. The angle formed when looking down from the horizontal
2. Special right triangle: isosceles right triangle where the legs are congruent and the hypotenuse = leg * sqrt(2)
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)
4. 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.
5. 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)

5 Multiple Choice Questions

1. 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
   1. Solve a triangle
   2. Obtuse triangle
   3. cosine
   4. Acute triangle
2. 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)
   1. tangent
   2. sine
   3. cosine
   4. SOH CAH TOA
3. 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
   1. Solve a triangle
   2. cosine
   3. Acute triangle
   4. Obtuse triangle
4. Special right triangle: hypotenuse = shorter side 2; longer side = shorter side sqrt(3)
   1. Acute triangle
   2. 30-60-90 right triangle
   3. 45-45-90 right triangle
   4. Solve a triangle
5. The angle formed when looking up from the horizontal
   1. SOH CAH TOA
   2. Inverse Trig Ratio
   3. Angle of depression
   4. Angle of elevation

5 True/False Questions

1. Pythagorean Triple → In a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2

   True        False

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.

   True        False

3. 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

   True        False

4. SOH CAH TOA → Mnemonic device to help remember the trig ratios in a right triangle: sin = opp/hyp; cos = adj/hyp; tan = opp/adj

   True        False

5. 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.

   True        False