Question

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

Answer 1

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Solution:

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

Therefore, AC = 25 cm

(i) We need to find Sin A and Cos A.

As we know, sine of angle is equal to the ratio of length of the opposite side and hypotenuse side. Therefore,

Sin A = BC/AC = 7/25

Again, cosine of an angle is equal to the ratio of adjacent side and hypotenuse side. Therefore,

cos A = AB/AC = 24/25

(ii) We need to find Sin C and Cos C.

Sin C = AB/AC = 24/25

Cos C = BC/AC = 7/25

Answer 2

sina = 7/25, cos a = 24/25

we have to find out the value of AC

AC = 25 from pythogoran triplet

sin c = 24/25, cos c= 7/25