Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 years ago

Determine z to the nearest tenth of a metre.

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

Relevance

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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• 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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• 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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