help find y.?

Attachment image

7 Answers

Relevance
  • 6 months ago

    By the cosine rule,

    y^2+37^2-2(37)ycos(42*)=31^2

    =>

    y^2-54.9927y+408=0

    =>

    y=46.2 or 8.8

    2 possibilities.

    • Pinkgreen
      Lv 7
      6 months agoReport

      Explanation: since x is a variable, it may be acute or obtuse, y is therefore has 2 solutions. Using the sine law, sin(x)/37=sin(42*)/31=>
      sin(x)=37sin(42*)/31=>sin(x)=0.79863975..=>x=53* or 127*. Thus
      y should have 46.2 or 8.8.

    • Login to reply the answers
  • 6 months ago

    Law of Sies:

    sin A / a = sin B / b = sin C / c

    sin 42/31 = sin x/37

    Angle ∠C = 85°

    The value of y:

    46.15245

    • Login to reply the answers
  • David
    Lv 7
    6 months ago

    Using the given formula x = 53 degrees and the length of y = 46.2 rounded to the nearest tenth

    • Login to reply the answers
  • They tell you to use the law of sines

    sin(42) / 31 = sin(x) / 37

    37 * sin(42) / 31 = sin(x)

    x = arcsin(37 * sin(42) / 31)

    x + 42 + Y = 180

    Y = 180 - 42 - x

    Y = 138 - x

    Y = 138 - arcsin(37 * sin(42) / 31)

    sin(Y) = sin(138 - arcsin(37 * sin(42) / 31))

    sin(Y) = sin(138)cos(arcsin(37 * sin(42) / 31)) - sin(arcsin(37 * sin(42) / 31)) * cos(138)

    sin(Y) = sin(138) * sqrt(1 - sin(arcsin(37 * sin(42)/31))^2) - cos(138) * (37 * sin(42) / 31)

    sin(Y) = sin(138) * sqrt(1 - (37 * sin(42) / 31)^2) - 37 * sin(42) * cos(138) / 31

    sin(Y) = sin(138) * (1/31) * sqrt(31^2 - 37^2 * sin(42)^2) - (1/31) * 37 * sin(42) * cos(138)

    sin(Y) = (1/31) * (sin(138) * sqrt(961 - 1369 * sin(42)^2) - 37 * cos(138) * sin(42))

    sin(Y) / y = sin(42) / 31

    y * sin(42) = 31 * sin(Y)

    y = 31 * sin(Y) / sin(42)

    y = 31 * (1/31) * (sin(138) * sqrt(961 - 1369 * sin(42)^2) - 37 * cos(138) * sin(42)) / sin(42)

    sin(138) = sin(42)

    y = sqrt(961 - 1369 * sin(42)^2) - 37 * cos(138)

    y = 46.152449588397384817605003643097

    y = 46.2

    • Login to reply the answers
  • How do you think about the answers? You can sign in to vote the answer.
  • 6 months ago

    you have the formula, just use it

    sin 42 / 31 = sin x/37

    sin x = (37/31) sin 42 = 0.7986

    x = 53º

    third angle = 180 – 42 – 53 = 85

    sin 85/y = sin 42 / 31

    y/sin 85 = 31/sin 42

    y = 31 sin 85 / sin 42 = 30.882 / 0.6691 = 46.2

    • Login to reply the answers
  • Mark
    Lv 7
    6 months ago

    It's after x and before z.

    • Login to reply the answers
  • 6 months ago

    y <--------- there it is

    • Login to reply the answers
Still have questions? Get your answers by asking now.