In a - ABC- if a -18- b -24- - -30 find cos A - cos B and cos C-

In a Δ ABC, we have cos A=b^2+c^2 a^2/2bc cos B=a^2+c^2 b^2/2ac cos C=a^2+b^2 c^2/2ab we have, a=18, b=24, c=30 Therefore, cos A=b^2+c^2 a^2/2bc=1152/1440= ...

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Standard XII

Mathematics

Conditional Identities

In a Δ ABC, i...

Question

$I n a Δ A B C, i f a = 18, b = 24, c = 30 f i n d c o s A, c o s B a n d c o s C .$

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Solution

$I n a Δ A B C, we have c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} c o s B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} we have, a = 18, b = 24, c = 30 Therefore, c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{1152}{1440} = \frac{4}{5} c o s B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{648}{1080} = \frac{3}{5} c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} = \frac{0}{864} = 0$

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In a ΔABC, if a=18, b=24, c=30 find cos A, cos B and cos C.

In a ΔABC, we havecos A=b2+c2−a22bccos B=a2+c2−b22accos C=a2+b2−c22abwe have,a=18, b=24, c=30Therefore,cos A=b2+c2−a22bc=11521440=45cos B=a2+c2−b22ac=6481080=35cos C=a2+b2−c22ab=0864=0

$I n a Δ A B C, i f a = 18, b = 24, c = 30 f i n d c o s A, c o s B a n d c o s C .$