In Fig 5.47, the value of is
(a)
(b)
(c)
(d)
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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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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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