From the top A of a vertical wall A B of height 30 m , the angles of depression of the top P and bottom Q of a vertical tower P Q are 15 ∘ and 60 ∘ respectively, B and Q are on the same horizontal level. If C is a point on A B such that C B = P Q , then the area (in m 2 ) of the quadrilateral B C P Q is equal to

Step-by-step solution

Given that from the top A of a vertical wall A B of height 30   m , the angles of depression of the top P and bottom Q of a vertical tower P Q are 15 ∘ and 60 ∘ respectively, B and Q are on the same horizontal level and C is a point on A B such that C B = P Q . The required diagram will be From the diagram, ⇒ tan 60 ° = A B B Q ⇒ 30 x = 3 ; ⇒ x = 10 3   m Also, tan 15 ° = A C C P ⇒ 30 - h x = 2 - 3 ⇒ 30 - h = 10 3 2 - 3 ⇒ 30 - h = 20 3 - 30 ⇒