Let P Q R S be a quadrilateral in a plane, where Q R = 1 , ∠ P Q R = ∠ Q R S = 70 ° , ∠ P Q S = 15 ° and ∠ P R S = 40 ° . If ∠ R P S = θ ° , P Q = α and P S = β , then the interval(s) that contain(s) the value of 4 α β sin θ ° is/are

Step-by-step solution

Given, P Q R S be a quadrilateral in a plane, where Q R = 1 , ∠ P Q R = ∠ Q R S = 70 ° , ∠ P Q S = 15 ° and ∠ P R S = 40 ° . If ∠ R P S = θ ° , P Q = α and P S = β , Now plotting the diagram of given values we get, Applying sine rule in ∆ P Q R we get, α sin 30 ° = 1 sin 80 ° ⇒ α = 1 2 sin 80 °                 . . . i Applying sine rule in ∆ P R S , β sin 40 2 = 1