SOLUTION: It says, "Sketch the triangle and use the Law of Cosines to find the indicated value. Round your answer to the nearest hundreth." Find the third side of a triangle with sides of

Algebra ->  Trigonometry-basics -> SOLUTION: It says, "Sketch the triangle and use the Law of Cosines to find the indicated value. Round your answer to the nearest hundreth." Find the third side of a triangle with sides of      Log On


   

Question 693459: It says, "Sketch the triangle and use the Law of Cosines to find the indicated value. Round your answer to the nearest hundreth."
Find the third side of a triangle with sides of 120cm and 100cm and an included angle of 47 degrees.
Find the angle opposite the longest side in a triangle with sides of 43ft, 48ft, and 65ft.
Find the two smaller angles in a triangle with sides of 7in, 7in, and 13in.
please help me
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
It says, "Sketch the triangle and use the Law of Cosines to find the indicated value. Round your answer to the nearest hundreth."
Find the third side of a triangle with sides of 120cm and 100cm and an included angle of 47 degrees.


The Side-Angle-Side version of the law of cosines is:

%28matrix%284%2C1%2C%0D%0ASide%2Copposite%2Cgiven%2Cangle%29%29%5E2 = %28matrix%286%2C1%2C%0D%0AFirst%2Cgiven%2Cside%2Cof%2Cgiven%2Cangle%29%29%5E2 + %28matrix%286%2C1%2C%0D%0ASecond%2Cgiven%2Cside%2Cof%2Cgiven%2Cangle%29%29%5E2 - 2·%28matrix%286%2C1%2C%0D%0AFirst%2Cgiven%2Cside%2Cof%2Cgiven%2Cangle%29%29·%28matrix%286%2C1%2C%0D%0ASecond%2Cgiven%2Cside%2Cof%2Cgiven%2Cangle%29%29·%28matrix%284%2C1%2C%0D%0ACosine%2Cof%2Cgiven%2Cangle%29%29



   x² = 120² + 100² - 2·(120)·(100)·cos(47°)
   x² = 14400 + 10000 - 16367.96064
   x² = 8032,039359
    x = 89.62164559 cm
Round to nearest hundredth:
    x = 89.62cm

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Find the angle opposite the longest side in a triangle with sides of 43ft, 48ft, and 65ft.


The Side-Side-Side version of the law of cosines is:

%28matrix%284%2C1%2C%0D%0ACosine%2Cof%2C+any%2C+angle%29%29 = 

cos(θ) = %2843%5E2%2B48%5E2-65%5E2%29%2F%282%2A43%2A48%29   

cos(θ) = %281849%2B2304-4225%29%2F4128

cos(θ) = -72%2F4128

cos(θ) = -0.0174418605

Find the inverse cosine

    θ = 90.99939567° round that to 91.00°

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Find the two smaller angles in a triangle with sides of 7in, 7in, and 13in.


You do this one by yourself.  It's a Side-Side-Side case and is done exactly
like the previous one. [The triangle is isosceles, that's why I labeled both
smaller angles the same, θ).

Edwin