Question
The length of the shadow of a vertical tower increases by 8 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find the height of the tower?
AB = 8 m DC = h, BC = x In ∆BCD tan 45 ° = DC/BC = h/x 1 = h/x x = h In ∆ACD tan 30° = DC/AC = DC/(AB + BC) 1/ √3 = h/(8 + x) 1/ √3 = h/(8 + h) 8 + h = √3 h √3 h - h = 8 h ( √3 - 1 ) = 8 h = 8/( √3 - 1) x ( √3 + 1)/ ( √3 + 1) = 4( √3 + 1)More Height and Distance Questions
- A man 1.5 m tall is 22.5 m away from a tower 24 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
- The angle of elevation of the top of a tower from a point on the ground is 30°. On moving 20 m closer to the tower, the angle of elevation becomes 45°. Fin...
- A tree of height 'h' meters is partially bent at a certain point above the ground, causing its top to touch the ground at a distance of 12 meters from its ...
- Two ships are on opposite sides in front of a lighthouse in such a way that all three of them are in line. The angles of depression of two ships from the t...
- A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elev...
- The angle of elevation of the top of a building from a point on the ground is 30° and moving 40 meters towards the building it becomes 60°. The height of t...
- A man 3 m tall is 19 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
- A tree stands tall with a height of 54 meters. From a point 'x' meters away from its base, the angle of elevation to the top of the tree is 60°. Determine ...
- If distance between two pillars of length 9 & 4 cm is x cm. If two angle of elevation of their respective top from a point on ground of other are complemen...
- Two buildings are collinear with the base of a tower and are at a distance 9m and 16m from the base of the tower. The angles of elevation from these two bu...
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
