math 2: triangle trigonometry

Question 1

sides of the 45-45-90 triangle:

Answer 1

legs: 1, 1
hypotenuse: √2

Question 2

sides of the 30-60-90

Answer 2

leg across from 30: 1
leg across from 60: √3
hypotenuse: 2

Question 3

special right triangles can be used to find trig values for special angles:

Answer 3

multiples of 30, 45, 60 (unit circle)

Question 4

you can also obtain trig values of quadrantal angles, which are

Answer 4

multiples of 90

Question 5

law of sines:

Answer 5

sinA/ a = sinB/ b = sinC/ c

Question 6

law of sines implies that the angles of a triangle and the lengths of the opposite sides are

Answer 6

proportional

Question 7

law of cosines (a² =)

Answer 7

a² = b² + c² - (2bc)(cosA)

Question 8

law of cosines (b² =)

Answer 8

b² = a² + c² - (2ac)(cosB)

Question 9

law of cosines (c² =)

Answer 9

c² = a² + b² - (2ab)(cosC)

Question 10

law of cosines is a generalization of the … with A, B, or C as the

Answer 10

pythagorean theorem; right angle

Question 11

the last term of the law of cosines represents the … for A, B, or C not being a …

Answer 11

“correction”’ right angle

Question 12

SSA case is the

Answer 12

ambiguous case

Question 13

case 1: there is no triangle if

Answer 13

a > b

Question 14

case 2: h =

Answer 14

bsinA

Question 15

case 2a: no triangle when

Answer 15

a

Question 16

case 2b: one obtuse triangle when

Answer 16

a > b

Question 17

case 2c: there are two possible triangles when a

Answer 17

a > h but a

Question 18

case 2d: there is one right triangle when

Answer 18

a = h

Question 19

area of triangle ABC is

Answer 19

1/2 cbsinA
1/2 acsinB
1/2 absinC