Math, asked by svarsha44, 11 months ago

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

Answers

Answered by pulakmath007
7

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

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1.In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971

2. If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

3. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

Answered by saranyaroyal2009
0

Step-by-step explanation:

this is clear explanation of problem

Attachments:
Similar questions