Assignment 2- Trigonometry (Heights and Distances)

Q1. Find the angle of elevation of the top of the tower of height 100m from a point at a distance of 100m from foot of the tower on a horizontal plane.

Q2. A kite is flying at a height of 75 m from the ground level, attached to a string inclined at 600 to the horizontal. Find the length of the string.

Q3. Two men are on opposite side of a tower. They measure the angle of elevation of the top of tower as 450 and 600 respectively. The height of tower is 30m. Find the distance between the two men.

Q4. A vertically straight tree, 15m high, is broken by wind in such a way that its top just touches the ground and makes an angle of 600 with the ground. At what height from the ground did the tree break?

Q5. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 5m. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are 300 and 600 respectively. Find height of the tower.

Q6. The horizontal distance between two towers is 70m. The angle of depression of top of the first tower when seen from the top of the second tower is 300. If the height of the second tower is 120m, find height of the first tower.

Q7. From the top of the tower 50m high the angles of depression of top and bottom of a pole are observed to be 450 and 600 respectively. Find height of the pole.

Q8. A man is standing on a deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of hill as 600 and the angle of depression of the base of hill as 300. Find the distance of the hill from ship and height of the hill.

Q9. A person standing on the bank of river observes that the angle of elevation of top of the tree standing on opposite bank is 600. When he moves 40m away from the bank, he finds the angle of elevation to be 300. Find height of the tree and also width of the river.

Q10. An aeroplane, when 3000m high, passes vertically above another aeroplane at an instant when the angles of elevation of two aeroplanes from the same point on the ground are 600 and 450 respectively. Find vertical distance between the two aeroplanes.

Q11. The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sunrays meet the ground at an angle of 600. Find the angle between the sunrays and ground at the time of longer shadow.

Q12. At a point on a level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192m towards the tower, the tangent of an angle is found to be 3/4. Find height of the tower.

Q13. An aeroplane flying horizontally 1km above ground is observed at an elevation of 600. After 10 seconds, its elevation is observed to be 300. Find speed of the plane.

Q14. The angle of elevation of a plane from the point on the ground is 600. After 15 seconds, the angle of elevation becomes 300. If the plane is at a constant height of

1500m, find the speed of it.

Q15.The angle of elevation of the top of a tower from a point A on the ground is 300. On moving a distance of 20m towards the foot of the tower to a point B the angle of elevation increases to 600. Find the height of the tower and the distance of the tower from the point A.