In a right angle triangle ABC with right angle at B, in which a = 24 units, b = 25 units and ∠BAC = θ. Then, find cosθ and tanθ.

We have

In ∆ABC, ∠ABC = 90° and ∠BAC = θ.

Using this information, we can say

AC = hypotenuse of the triangle

BC = perpendicular (side opposite to the angle θ or ∠BAC)

Using Pythagoras theorem,

(hypotenuse)² = (perpendicular)² + (base)²

⇒ (25)² = (24)² + (base)²

⇒ (AB)² = 625 – 576

⇒ (AB)² = 49

⇒ AB = √49 = 7 units

So, we have AB = 7 units, BC = 24 units and AC = 25 units.

Thus,

⇒

And

⇒

Thus, and .