Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 years ago

Please Help!! Finding the length of the missing side in the triangle. 10 points!?

Determine z to the nearest tenth of a metre.

http://i.imgur.com/D2Lc0lX.jpg

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  • 4 years ago
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    AB: side c → given: c = 18.5

    BC: side a = z

    AC: side b → given: b = 15

    A = 89 ° ← this is the angle at the point A

    B ← this is the angle at the point B

    C ← this is the angle at the point C

    z.cos(C) + c.cos(A) = b

    z.cos(C) = b - c.cos(A)

    Law of cosinus, whatever the triangle:

    https://fr.wikipedia.org/wiki/Loi_des_cosinus

    c² = a² + b² - 2ab.cos(C) → in our case: a = z

    c² = z² + b² - 2zb.cos(C)

    z² = c² - b² + 2.(zb).cos(C) → recall: z.cos(C) = b - c.cos(A)

    z² = c² - b² + 2b.[b - c.cos(A)]

    z² = c² - b² + 2b² - 2bc.cos(A)

    z² = c² + b² - 2bc.cos(A)

    z² = 18.5² + 15² - 555.cos(89)

    z² = 567.25 - 555.cos(89)

    z² ≈ 557.56291

    z ≈ 23.6127913

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  • 4 years ago

    Side 1: 15 opposite angle: 39.431°

    Side 2: 23.613 opposite angle: 89°

    Side 3: 18.5 opposite angle: 51.569°

    Total Area: 138.72886770295

    http://www.calculator.net/triangle-calculator.html...

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  • 4 years ago

    You can use law of cosines for that. "z" is opposite of the given angle, so:

    c² = a² + b² - 2ab cos(C)

    z² = 18.5² + 15² - 2(18.5)(15) cos(89)

    z² = 342.25 + 225 - 555 cos(89)

    z² = 567.27 - 555 cos(89)

    z² = 567.27 - 555(0.0174524)

    z² = 567.27 - 9.686082

    z² = 557.583918

    z = 23.6 m (rounded to 1DP)

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