Advertisements
Advertisements
प्रश्न
A man observes the angle of elevation of the top of the tower to be 45°. He walks towards it in a horizontal line through its base. On covering 20 m the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.
उत्तर
Let the height of the tower be ‘h’ m.
In Δ ADC , tan 45° = `h/(20 + x)`
1 = `h /(20+ x`
⇒ h = 20 + x
Also , In ΔBDC , tan 60° = `h/x`
`sqrt(3) = h / x`
⇒ x = `h/(sqrt(3))` ...(2)
h = 20 + `h/sqrt(3)`
`h - h/sqrt(3) = 20`
`h((sqrt(3) -1)/sqrt(3)) = 20`
`h = (20 sqrt(3)) /((sqrt(3) - 1)) xx ((sqrt(3) + 1)) /(( sqrt(3) +1 )`
`= (20 (3 + sqrt(3)))/(3-1)`
`= (20 (3+1.732))/2`
= 10 (4.732)
Height of the tower . h = 47.32 m
APPEARS IN
संबंधित प्रश्न
A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 68° with the ground. Find the height, upto which the ladder reaches.
Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32°24′ with the pole and when it is turned to rest against another pole, it makes angle 32°24′ with the road. Calculate the width of the road.
Two pillars of equal heights stand on either side of a roadway, which is 150 m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60° and 30°; find the height of the pillars and the position of the point.
A man on a cliff observes a boat, at an angle of depression 30°, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the boat sails at a uniform speed, determine:
- how much more time it will take to reach the shore?
- the speed of the boat in metre per second, if the height of the cliff is 500 m.
A vertical pole is 90m high and the length of its shadow is `90sqrt(3)`. what is the angle of elevation of the sun ?
The top of a palm tree having been broken by the wind struck the ground at an angle of 60° at a distance of 9m from the foot of the tree. Find the original height of the palm tree.
A vertical tow er stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the ft agstaff is 45°. Find the height of the tower.
A boy is standing on the ground and flying a kite with 100m of sting at an elevation of 30°. Another boy is standing on the roof of a 10m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet.
The angle of elevation of a tower from a point 200 m from its base is θ, when `tan θ = 2/5`. The angle of elevation of this tower from a point 120m from its base is `Φ`. Calculate the height of tower and the value of `Φ`.
Of the two trees are on either side of a river, one of them is 50m high. From the top of this tree the angles of depression of the top and the foot of the other tree are 30° and 60° respectively. Find the width of the river and the height of the other tree.
