# If then find the values cos θ and tan θ.

Given:

We know that,

Or

Let,

Perpendicular =AB =3k

and Hypotenuse =AC =5k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

(AB)2 + (BC)2 = (AC)2

(3k)2 + (BC)2 = (5k)2

9k2 + (BC)2 = 25k2

(BC)2 = 25 k2 – 9 k2

(BC)2 = 16 k2

BC =16 k2

BC =±4k

But side BC can’t be negative. So, BC = 4k

Now, we have to find the value of cos θ and tan θ

We know that,

The side adjacent to angle θ = BC =4k

Hypotenuse = AC =5k

So,

Now, tan θ

We know that,

Perpendicular = AB =3k

Base = BC =4k

So,

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