Advertisements
Advertisements
प्रश्न
The length of a string between a kite and a point on the ground is 90 meters. If the string makes an angle O with the ground level such that tan O = 15/8, how high is the kite? Assume that there is no slack in the string.
उत्तर
Length of string between the point on ground and kite = 90
Angle made by the string with the ground is θ and `tan theta = 15/8`
`=> theta = tan^(-1) (15/8)`
The height of the kite be Hm
If we represent the above data in the figure as shown then it forms right-angled triangle ABC.
We have,
`tan theta = (AB)/(BC)`
`=> 15/8 = H/(BC)`
`=> BC = 84/15` .......(1)
In ΔABC , by Pythagoras theorem we have
`AC^2 = BC^2 + AB^2`
`=> 90^2 = ((8H)/(15))^3 + H^2`
`=> 90^2 = ((8H)^2 + (15H)^2)/15^2`
`=> H^2 (8^2 + 15^2) = 90^2 xx 15^2`
`=> H^2 (64 + 225) = (90 xx 15)^2`
`=> H^2 = (90 xx 15)^2/289`
`= H^2= ((90 xx 15)/17)^2`
`=> H = (90 xx 15)/17 = 79.41`
∴ height of kite from ground H = 79.41 m
APPEARS IN
संबंधित प्रश्न
From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 meters. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 300 and 600. Find the height of the tower.
A kite is flying at a height of 75 in from the level ground, attached to a string inclined at 60°. to the horizontal. Find the length of the string, assuming that there is no slack in it.
[Take `sqrt(3)` =1.732 ]
The ratio of the length of a rod and its shadow is `1 : sqrt3`. The angle of elevation of the sum is
If two circles having centers P and Q and radii 3 cm and 5 cm. touch each other externally, find the distance PQ.
From the top of a rock `50sqrt(3)` m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock
A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)
A portion of a 60 m long tree is broken by a tornado and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to ____________.
As observed from the top of a 150 m high lighthouse from the sea level, the angles of depression of the two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
