Larry baked 3 times as many sugar cookies as peanut butter cookies. he baked 96 cookies in all. how many did he bake in all

Larry baked 3 times as many sugar cookies as peanut butter cookies. It means for every 4 cookies there will be 3 sugar cookies and 1 peanut butter cookie. Then for 96 cookies the number of sugar and peanut butter cookie would be:

sugar cookies = 96 cookies *3/4 = 72 cookies
peanut butter cookies= 96 cookies* 1/4  = 24 cookies

He baked 96 cookies in all.

96*(1/(1+3))=24 peanut cookies
96*(3/(1+3))=72 sugar cookies.
Also, he baked 24 peanut cookies, 72 sugar cookies.

  a) a = 7.37, b = 15.13, C = 67°

  b) 1 triangle

Step-by-step explanation:

a)

Two angles and one side are given. That means the triangle is uniquely determined, and the remaining sides can be found from the Law of Sines.

The third angle is ...

  C = 180° -A -B = 180° -29° -84° = 67°

Then the Law of Sines tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

  a = sin(A)/sin(C)·c = sin(29°)/sin(67°)·14 ≈ 7.37

  b = sin(B)/sin(C)·c = sin(84°)/sin(67°)·14 ≈ 15.13

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b)

Ordinarily, when the given angle (B = 30°) is opposite the shorter of the given sides (b = 10 < a = 20), it means there are two possible solutions to the triangle.

However, when the sine of the angle is exactly equal to the ratio of the given sides: sin(30°) = 10/20 = 1/2, the larger angle can only be 90°. That is, the one triangle that can be formed is a right triangle.

The Law of Sines tells you this.

  sin(A)/a = sin(B)/b

  sin(A) = (a/b)sin(B) . . . . . . multiply by 'a'

  A = arcsin(a/b·sin(B)) = arcsin(20/10·sin(π/6)) = arcsin(1)

  A = 90°