# Heights and Distance

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Q1. If the angle of elevation of the top of a coconut tree from a point on the ground is 60 ° and the point is 20 meters away from the foot of the tree, let us find the height of the tree.

Q2. The length of the shadow of a tower is 9 meters when the sun’s angle of elevation is 30 °. Let us write by calculating the height of the tower.

Q3. A kite is flying with a thread of 150 meters length from a field. If the thread of kites makes an angle 60 ° with horizontal line, let us write by calculating the height of the kite from the ground.

Q4. A palm tree stands on the bank of a river. A post is fixed in the earth on the other bank just opposite to the palm tree. On moving 7 √3 meters from its foot the post along the bank, it is found that the tree makes an angle of 60 ° at that point with respect to this bank. Let us find the width of the river.

Q5. A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8 √3 meters from its foot and makes an angle of 30 °. Let us write by calculating at what the height the post is bent and what is the height of the post.

Q6. Two houses stand just on the opposite’s sides of a road of our village. A ladder that stands against the wall of the first house is at a distance of 6 meters from the house and makes an angle of 30 ° with the horizontal line. But if the ladder stands against the wall of the second house keeping its foot at the sone point, it makes an angle of 60 ° with the horizontal line.

(i)                 Let us find the length of the ladder.

(ii)              Let us write by calculating, the distance of the foot of the ladder from the foot of the wall of the second house.

(iii)            Let us find the width of the road.

(iv)            Let us find the height where the top of the ladder is fixed against the wall of the second house.

Q.7 If the angle of the elevation of the top of a chimney from a point om the horizontal plane passing through the foot of the chimney id 60 ° and the angle of elevation from another point ion the same plane at a distance of 24 meters from the first point is 30 °, let us write by calculating the height of the chimney.
[ Let us find the approximate value correct up to three decimal places, assuming √3 = 1.732 approx.)]

Q.8 The length of the shadow of a post becomes 3 meters smaller when the angle of elevation of the sun increases from 45 ° to 60 °. Let us find the height of the post.
[ Let us find the approximate value correct up to three decimal places, assuming √3 = 1.732 approx.)]

Q9. When the top of the chimney of a factory is seen from a point on the roof of the three storied building of 9√3-meter height, the angle of elevation is 30 °. If the distance between the factory and chimney is 30 meters, let us write by calculating height of the chimney.

Q10. The bottom of a light house and bottom of the mast of two shops are on the same straight line and the angle of depression from the light house at the bottom of mat of two hip are 60 ° and 30 ° respectively. If the distance of the points at the bottom of the light house and the bottom of the mast of other ship from the light house be and what will the height of light house be.

Q11. From a point on the roof of five-storied building the angle of elevation of the top of a monument and that of angle of depression of the foot of the monument are 60 ° and 30 ° respectively. If the height of the building is 16 meters, let us write by calculating the height of the monument and the distance of the building from the monument.

Q12. I am flying a kite having the length of thread 250 meters, when the threads make an angle 60 ° with the horizontal line, and when the thread make an angle of 45 ° with the horizontal line, let us write by calculating in each case what is the height of kite from me. Let us find in which of the two cases will be kite be at a greater height from the other.

Q13. A passenger of on aero plane observes that Howrah station is at one side of the plane and Saheed minor Is just opposite side. The angle of depression of Howrah station and Shaheed minar from the passenger of aero plane are 60 ° and 30 ° respectively. If the aero plane is at a height of 545 √3 meters at that time, let us find the distance between Howrah station and Shaheed minar.

Q14. The length of the flag at the roof of three-storied building in 3.3 meter from any point of road the angles of elevation of the top and foot of the flag post are 50° and 45 °. Let us write by calculating the height of three-storied building. [Let, tan50 °=1.192]

Q15. The heights of two towers are 180 meters and 60 meters respectively. If the angle of elevation of the top of the first tower from the foot of the second tower is 60 °, let us write by calculating what is the angle of elevation of the top of the second tower from the foot of the first.

Q16. The length of shadow of a tower standing on the ground is found to be 60 meters more when the sun’s angle of elevation changes from 30 ° to 60 °, let us find the height of the tower.

Q17. From a point on the same plane along the horizontal line passes through the foot of a chimney, the angle of elevation of the top of the chimney is 30 ° and the angle of elevation of the top of the chimney is 60 ° at a point on the same straight line proceeding 50 meters to the chimney. Let u write by calculating the height of the chimney.

Q18. A vertical pot of 126 dm height was bent at some point above the ground and it just touched the ground making an angle of 30 ° with the ground. Let u write by calculating what height was post bent and at what distance did it meet the ground from the foot of the post.

Q19. Mohit, standing in the midst of a field, observes a flying bird in his north at an angle of elevation of 30 ° and after 2 minutes he observes the bird in his south at an angle of elevation of 60 °. If the bird flies in a straight line all along at a height of 50 √ 3 meters, let us find it speed in kilometer per hour.

Q20. Amitadidi standing on a railway overbridged of 5 √3-meter height observed the engine of the train from one side of the bridge at an angle of depression of 30 °. But jut after 2 seconds, she observed the engine at an angle of depression of 45 ° from the other side of the bridge. Let us find the speed of the train in meters per second.

Q21. A bridge is situated at right angle to the bank of the river. if one moves away a certain distance from the bridge along this side of the river, the other end of the bridge is seen at an angle of 45 ° and if someone moves a further distance of 400 meters in the same direction, the other end is seen at an angle of 30 °. Let us find the length of the bridge.

Q22. A house of 15 meters height, stand on one ide of a park and from a point on the roof of the houe the angle of depression of the foot of the chimney of brick kiln of the other side is 30 ° and the angle of elevation of the top of the chimney of brick kiln Is 60 °. Let us write the height of the chimney and the distance between the brick kiln and the house.

Q23. If the angle of depression of two consecutive mile stones on a road from an aero plane are 60 ° and 30 ° respectively, let us find the height of the aero plane, (i) when the two-mile stones stand on opposite side of the aero plane, (ii) when the two-mile stone stand on the same side of the aero plane.

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