Math, asked by maahira17, 9 months ago

In Fig 5.47, the value of cos\Phi is
(a)\frac{5}{4}
(b)\frac{5}{3}
(c)\frac{3}{}
(d)\frac{4}{5}

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Answered by nikitasingh79
3

Given : From figure 5.47, AB (P) = 4 , BC (B) = 3 , AC (H) = 5

To find : the value of cos ϕ is

Solution :  

 We know that the sum of the angles of the straight line is 180°.

∴ ∠ θ + ∠90° + ∠ϕ = 180°

∠ θ  + ∠ϕ = 180° - 90°

∠ θ + ∠ϕ = 90°

∠ θ  = 90° - ∠ϕ ……….(1)

 

In ∆ABC,

sin θ = P/H = 4/5  

From eq 1 we obtain ,  

sin (90 - ϕ) = 4/5

We know that sin (90° -  θ ) = cos θ  

Sin (90 - ϕ) = cos ϕ  

∴ cos ϕ = 4/5

Hence the value of cos ϕ is ⅘ .

Among the given options option (D) ⅘ is  correct.

Hope this answer will help you…

 

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Answered by Pakiki
23

☺☺Hope it's help you☺☺

We know that the sum of all the angles on one side of a straight line is 180° . These angles are said to be in linear pair.

Therefore, using the figure, we get

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