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

Solution for Question 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A / (ii) sin C, cos C.

Solution for **Question 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A / (ii) sin C, cos C.**

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

Given: AB = 24 cm and BC = 7 cm

According to the Pythagoras Theorem,

In a right-angled triangle, the squares of the hypotenuse side are equal to the sum of the squares of the other two sides.

**By applying Pythagoras theorem, we get**

AC2=AB2+BC2

AC2 = (24)2+72

AC2 = (576+49)

AC2 = 625cm2

AC = √625 = 25

**Therefore, 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 = 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