If a = 18, b = 24 and c = 30, then find the value of cos A.

Concept:

Trigonometry:

• By definition, in a right-angled triangle with length of the side opposite to angle θ as perpendicular (P), base (B) and hypotenuse (H):

  sin θ = \( \rm \frac{P}{H}\), cos θ = \( \rm \frac{B}{H}\), tan θ = \( \rm \frac{P}{B}\).

• In general, if the angles of a triangle are named A, B and C, then the sides opposite to these angles are named a, b and c respectively.

Calculation:

The given sides of the triangle a = 18, b = 24 and c = 30 are 6 times 3, 4 and 5 respectively, which is a right-angled triangle with C = 90^∘.

Now, using the definition of trigonometric ratios, cos A = \( \rm \frac{b}{c}\) = \( \rm \frac45\).