If a = 2 , b = 3 , c = 4 in a triangle A B C , then cos C =

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If

a = 2, b = 3, c = 4

in a triangle

A B C

, then

\cos C =

MathematicsProperties of TrianglesAP EAMCETAP EAMCET 2022 (04 Jul Shift 2)

Options:

A $\frac{1}{4}$
B $\frac{- 1}{4}$
C $\frac{1}{2}$
D $\frac{- 1}{2}$

Solution:

2912 Upvotes Verified Answer

The correct answer is:

\frac{- 1}{4}

Given:
$a = 2, b = 3, c = 4$
Now,
$\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$
$\Rightarrow \cos C = \frac{4 + 9 - 16}{2 \times 2 \times 3}$
$\Rightarrow \cos C = \frac{- 3}{2 \times 2 \times 3}$
$\Rightarrow \cos C = - \frac{1}{4}$

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