If tan θ =0.75, then find the value of sin θ.

We know that,

Or

Given: tan θ =0.75

Let,

The side opposite to angle θ =BC = 3k

The side adjacent to angle θ =AB = 4k

Firstly we have to find the value of AC.

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

⇒ (AB)² + (BC)² = (AC)²

⇒ (4k)² + (3k)² = (AC)²

⇒ (AC)² = 16 k² +9 k²

⇒ (AC)² = 25 k²

⇒ AC =√25 k²

⇒ AC =±5k

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

Now, we will find the sin θ

Side opposite to angle θ = BC = 3k

and Hypotenuse = AC = 5k

So,