Question

If a = 20, b = 21 and cos c = 4/5 then c =

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{a = 20 \: , \: b = 21 \: , \: \cos C = \frac{4}{5} }$

TO DETERMINE

The value of c

FORMULA TO BE IMPLEMENTED

We are aware of the formula on Trigonometry that

$\displaystyle \sf{\cos C = \frac{ {a}^{2} + {b}^{2} - {c}^{2} }{2ab} }$

EVALUATION

Here it is given that

$\displaystyle \sf{a = 20 \: , \: b = 21 \: , \: \cos C = \frac{4}{5} }$

Now

$\displaystyle \sf{\cos C = \frac{ {a}^{2} + {b}^{2} - {c}^{2} }{2ab} }$

$\displaystyle \sf{ \implies \: \frac{4}{5} = \frac{ {(20)}^{2} + {(21)}^{2} - {c}^{2} }{2 \times 20 \times 21} }$

$\displaystyle \sf{ \implies \: {(20)}^{2} + {(21)}^{2} - {c}^{2} = \frac{4}{5} \times 2 \times 20 \times 21 }$

$\displaystyle \sf{ \implies \: {(20)}^{2} + {(21)}^{2} - {c}^{2} =32 \times 21 }$

$\displaystyle \sf{ \implies \: {c}^{2} = {(20)}^{2} + {(21)}^{2} - (32 \times 21 ) }$

$\displaystyle \sf{ \implies \: {c}^{2} = 400 + 441 - 672}$

$\displaystyle \sf{ \implies \: {c}^{2} = 169}$

$\displaystyle \sf{ \implies \: c = 13}$

FINAL ANSWER

Hence the required value of c = 13

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Answer 2

Step-by-step explanation:

this is clear explanation of problem