Advertisements
Advertisements
प्रश्न
A flag pole ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find radius of the dome `(sqrt(3) = 1.732)`
उत्तर
Height of the Flag pole (ED) = h m
AF and AD is the radius of the semi circle (r)
AC = (r + 7)
AB = (r + 7 + 5)
= (r + 12)
In the right ∆ABD, tan 30° = `"AD"/"AB"`
`1/sqrt(3) = r/("r" + 12)`
`sqrt(3` r = r + 12
`sqrt(3)` r − r = 12
⇒ `"r" (sqrt(3) - 1)` = 12
r[1.732 – 1] = 12
⇒ 0.732r = 12
r = `12/(0.732)` ⇒ = 16.39 m
In the right ∆ACE, tan 45° = `"AE"/"AC"`
`1 + ("r" + "h")/("r" + 7)`
r + 7 = r + h
∴ h = 7 m
Radius of the dome (r) = 16.39 m
APPEARS IN
संबंधित प्रश्न
There are three stair-steps as shown in the figure below. Each stair step has width 25 cm, height 12 cm and length 50 cm. How many bricks have been used in it, if each brick is 12.5 cm x 6.25 cm x 4 cm?
The horizontal distance between two towers is 60 meters. The angle of depression of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 90 meters. Find the height of the first tower.
From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is
From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is
Two persons are a metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter post is
Three villagers A, B and C can see each other using telescope across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate the vertical height between B and C. (tan 20° = 0.3640, `sqrt3` = 1.732)
If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1: h2 = ____________.
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
Let AB and PQ 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 PQ is twice the height of pole AB, then, tan2 θ is equal to ______.
Read the following passage:
|
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure; On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is 30° and the angle of elevation of the top of Section A is 45°.
|
Based on the above information, answer the following questions:
- Find the length of the wire from the point O to the top of Section B.
- Find the distance AB.
OR
Find the area of ∠OPB. - Find the height of the Section A from the base of the tower.
