# 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,

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