Question

Two adjacent sides of a parallelogram have lengths a and b and the angle between these two sides is theta. Express the area of the parallelogram in terms of a, b, and theta

Answer 1

Answer:

A = a*b*Cos(θ-90º)

Step-by-step explanation:

Area of a parallelogram : A = b*h, where h is the height

h form 90º angle with b.

h = a*Cos (θ-90º) in a sub-triangle formed by h, a and a*Sin(θ-90º)

In the Pythagoearn identity for this sub-triangle:

(a*Sin(θ-90º))² + (a*Cos(θ-90º))² = a²

(a*Sin(θ-90º))² + h² = a²

h² = a² (1 - Sin² (θ-90ª))

h² = a² (Cos²(θ-90º)

h = a (Cos (θ-90º))