Question

If a=26cm.,b=30cm. and cos C=63/65, then find c.​

Answer 1

Answer:

The required value is " c = 8 ".

Given that

In ΔABC, If a = 26 cm, b = 30 cm, cos C = 63/65

We know that

\begin{lgathered}cosC=\frac{a^{2}+b^{2}-c^{2} }{2ab}\\ \\cosC=\frac{26^{2}+30^{2}-c^{2}}{2(26)(30)}\\\\\frac{63}{65} =\frac{1576-c^{2}}{1560}\\\\\frac{63}{65}(1560) =1576-c^{2}\\\\1512=1576-c^{2}\\\\c^{2}=1576-1512\\\\c^{2}=64\\\\c=8\end{lgathered}

cosC=

2ab

a

2

+b

2

−c

2

cosC=

2(26)(30)

26

2

+30

2

−c

2

65

63

=

1560

1576−c

2

65

63

(1560)=1576−c

2

1512=1576−c

2

c

2

=1576−1512

c

2

=64

c=8

Answer 2

$c { }^{2} = a {}^{2} + b ^{2} - 2ab \: \: cos \: c$

c

$c^{2} = (26) {}^{2} + (30) { }^{} { }^{2} - 2 \times 26 \times 30 \times 63upon \: 65$

$c {}^{2} = 64$

$c = 8$

Step-by-step explanation:

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