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In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C

In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given:
​AB = 24 cm and BC = 7 cm

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

By applying Pythagoras theorem,
In a right- angled triangle, the squares of the hypotenuse side is equal to the sum of the squares of the[page1image1641698352]other two sides.
we get
AC^2=AB^2+BC^2
AC^2= (24)^2+7^2
AC^2= (576+49)

AC^2= 625cm^2
AC =√625 = 25 Therefore, AC = 25 cm



(i) To find Sin (A), Cos (A)
We know that sine (or) Sin function is the equal to the ratio of length of the opposite side to the hypotenuse side. So it becomes
Sin (A) = Opposite side /Hypotenuse = BC/AC = 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 = AB/AC = 24/25

(ii) To find Sin (C), Cos (C) Sin (C) = AB/AC = 24/25 Cos (C) = BC/AC = 7/25

Thanks

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