(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,
(iii) tan A – cot C
We know that,
tan A
Here, θ = A
Side opposite to ∠A = BC = 5
Side adjacent to ∠A = AB = 12
Cot C
Here, θ = C
Side adjacent to ∠C = BC = 5
Side opposite to ∠C = AB = 12