In ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine

a. sin A, cos A

b. sin C, cos C

(i)

(a) sin A

We know that,

So, here θ = A

Side opposite to ∠A = BC = 7

Hypotenuse = AC = ?

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem.

According to Pythagoras theorem,

(Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (AB)² + (BC)² = (AC)²

⇒ (24)² + (7)² = (AC)²

⇒ 576 + 49 = (AC)²

⇒ (AC)² = 625

⇒ AC =√625

⇒ AC =±25

But side AC can’t be negative. So, AC = 25cm

Now, BC = 7 and AC = 25

So,

Cos A

We know that,

So, here θ = A

Side adjacent to ∠A = AB = 24

Hypotenuse = AC = 25

So,

(b) sin C

We know that,

So, here θ = C

The side opposite to ∠C = AB = 24

Hypotenuse = AC = 25

So,

Cos C

We know that,

So, here θ = C

Side adjacent to ∠C = BC = 7

Hypotenuse = AC = 25

So,