From the given figure, find the value of

(i) sin θ

(ii) tan θ

(iii) tan A – cot C

(i) sin θ

We know that,

Side opposite to θ = BC = ?

Hypotenuse = AC = 13

Firstly we have to find the value of BC.

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

According to Pythagoras theorem,

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

⇒ (AB)² + (BC)² = (AC)²

⇒ (12)² + (BC)² = (13)²

⇒ 144 + (BC)² = 169

⇒ (BC)² = 169–144

⇒ (BC)² = 25

⇒ BC =√25

⇒ BC =±5

But side BC can’t be negative. So, BC = 5

Now, BC = 5 and AC = 13

So,

(ii) tan θ

We know that,

Side opposite to θ = BC = 5

Side adjacent to θ = AB = 12

So,

(iii) tan A – cot C

We know that,

and

tan A

Here, θ = A

Side opposite to ∠A = BC = 5

Side adjacent to ∠A = AB = 12

So,

Cot C

Here, θ = C

Side adjacent to ∠C = BC = 5

Side opposite to ∠C = AB = 12

So,

So,