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law of cosine

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In triangle PQR, if r=4, q=5 and cos P= -2/5, find p in simplest radical form
asked Nov 22, 2013 in TRIGONOMETRY by linda Scholar

2 Answers

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Given PQR triangle.

Sides are r = 4, q = 5

Use law of cosines p^2 = q^2+r^2-2qr CosP

p^2 = (5)^2+(4)^2-2(5)(4) Cos(-2/5)

p^2 = 25+16-40 Cos(-0.4)

p^2 = 1Cos(0.4)

p^2 = 0.99

p = Sqrt(0.99)

 

 

answered Jan 25, 2014 by friend Mentor

Solution in simplest radical form image.

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In PQR triangle P,Q,R are angles and sides are p,q,r.

From law of cosines image

Substitute r = 4, q = 5 and P = -2/5 in above formula.

image

cos(-x) = cosx

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Apply squre root on each side.

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By using calculator image

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Solution in simplest radical form image.

answered Jun 13, 2014 by david Expert

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