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?Solution
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)
The angle of depression of a point on the ground as seen from the top of a tower, 65 feet high, is 45°. Find the distance of the point on the ground fr...
The angle of elevation of an aeroplane from a point on the ground is 60°. After 12 seconds flight the elevation changes to 30°, if the aeroplane...
A boat is being rowed away from a cliff 183 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 minute...
From a point on the ground, the angle of elevation of the top of a tower is 30 degrees. After moving 20 m towards the tower, the angle becomes 60 degree...
A man 3 m tall is 23 m away from a tower 26 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
From a point 30 m away, the angle of elevation of top of tower is 45°. Find height of tower.
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 th...
From the top of a lighthouse, the angle of depression to the top and bottom of a tower is 30° and 45°, respectively. If the lighthouse is 210 me...
The distance between two parallel poles is 65√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 3...
The angle of depression of a point on the ground as seen from the top of a tower, 35 feet high, is 45°. Find the distance of the point on the ground fr...
Relevant for Exams:
