Question

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In the given ∆ABC it is given that \angle∠ B = 90° .AB = 24 cm and BC = 7 cm than find the Value of Cos A = ? .




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Answer 1

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In a given triangle ABC, right-angled at B = ∠B = 90°

Given

AB = 24 cm

BC = 7 cm

According to the Pythagoras Theorem, in a right-angled triangle, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides.

By applying the Pythagoras theorem, we get

AC2= AB2+ BC2

AC2 = (24)2+72

AC2 = (576+49)

AC2 = 625cm2

AC = √625

AC = 25

∴ AC = 25 cm

(i) To find Sin (A), Cos (A)

We know that the sine (or) Sin function is equal to the ratio of the length of the opposite side to the hypotenuse side. So it becomes

Sin (A) = Opposite side /Hypotenuse

Sin (A) = BC/AC

Sin (A) = 7/25

Cosine or Cos function is equal to the ratio of the length of the adjacent side to the hypotenuse side and it becomes,

Cos (A) = Adjacent side/Hypotenuse

Cos (A) = AB/AC

Cos (A) = 24/25

(ii) To find Sin (C), Cos (C)

Sin (C) = AB/AC

Sin (C) = 24/25

Cos (C) = BC/AC

Cos (C) = 7/25

Answer 2

Answer:

Draw a triangle using given instructions:

From figure: Δ ABC is a right angled triangle

By Pythagoras theorem:

AC2 = BC2 + AB2AC = 25

(i) Find sin A sin A = BC/AC = 7/25

(ii) Find cos A cos A = AB/AC = 24/25

(iii) sin C = AB/AC = 24/25

(iv) cos C = BC/AC = 7/25

Step-by-step explanation:

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