5.5/5.6 (Nonright Triangles)

Question 1

What is the law of sines?

Answer 1

(a/sin A)=(b/sinB)=(c/sin C)

Question 2

What is the law of cosines?

Answer 2

c^2=a^2+b^2-2ab sinC, where C is the largest angle

Question 3

How do you find the area of a triangle given ASS? How many answers are there?

Answer 3

(1/2)ab sinC; 2 (even though the calculator will only give one)

Question 4

How do you find area of a triangle given three sides?

Answer 4

Herons; s=(a+b+c)/2, k=/sqrt[s(s-a)(s-b)(s-c)]

Question 5

What is the derivation of the Law of Sines?

Answer 5

Drawing an amplitude and equating sin of two angles.

Question 6

What is the derivation for the Law of Cosines?

Answer 6

applying the distance formula from (a,0) to (x,y) but replacing the latter with (cCosB,cSinB)

Question 7

How should you check the answer at the end of a Law of Sines question with two answers?

Answer 7

If two of the known angles add up to less than 180 degrees