If 15 cot A=18, find sin A and sec A.

Given: 15 cot A = 8

And we know that,

Or

Let,

Side adjacent to angle A =AB = 8k

The side opposite to angle A =BC = 15k

where k is any positive integer

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

⇒ (8k)² + (15k)² = (AC)²

⇒ (AC)² = 64 k² +225 k²

⇒ (AC)² = 289 k²

⇒ AC =√289 k²

⇒ AC =±17k

But side AC can’t be negative. So, AC = 17k

Now, we will find the sin θ

Side opposite to angle θ = BC = 15k

and Hypotenuse = AC = 17k

So,

Now, we know that,

The side adjacent to angle θ = AB =8

Hypotenuse = AC =17

So,