Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202228 Jun 2022Morning ShiftMathematicsHeights and DistancesActual

Let A B and P Q be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q , which are feet of these two poles. Let π 8 and θ be the angles of elevation from C to P and A , respectively. If the height of pole P Q is twice the height of pole A B , then tan 2 θ is equal to

Options

  1. A3 - 2 2 2
  2. B3 + 2 2
  3. C3 - 2 2 4
  4. D3 - 2 4

Correct answer

C. 3 - 2 2 4

Step-by-step solution

From the given information in the question we can draw the following diagram Let B C = C Q = x   &   A B = h and P Q = 2 h So tan θ = h x and tan π 8 = 2   h x ⇒ tan θ tan π 8 = 1 2 ⇒ tan θ = 1 2 2 - 1 ⇒ tan 2 θ = 1 4 3 - 2 2

Practice Heights and Distances on Quantrex Academy →

More from Heights and Distances

The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower is 45 ° and from the feet of another person standing due west of the 2023From 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 2023The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is cos - 1 3 13 . If the distance of 2022A horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that ∠ P A O = ∠ P B O = 15 ° and &#8 2022The angle of elevation of the top P of a vertical tower P Q of height 10 from a point A on the horizontal ground is 45 ° . Let R be a point on A Q and from a point B , vertica 2022Let a vertical tower A B of height 2 h stands on a horizontal ground. Let from a point P on the ground a man can see upto height h of the tower with an angle of elevation 2 α 2022A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that Q R = 15 m . If from a point A on the ground the angle of 2022From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60 ° . The pole subtends an angle 30 ° at the top of the tower. Then the heigh 2022 Full Heights and Distances list All JEE Main PYQs