Angles of elevation and depression

Grade 9           Angles of elevation and depression                                                                 work sheet

(1) In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10^o. Find the height of the tree.

(2) A man standing on top of a mountain 1200 m high observes the angle of depression of a steeple to be 43^o. How far is the steeple from the mountain?

(3) A ladder is placed on horizontal ground with its foot 2 m from a vertical wall. If the ladder makes an angle of 50^o with the ground, find (a) the length of the ladder, 

     (b) the height of the wall. Give answers correct to 1 d.p.

(4) The length of the shadow of a vertical pole is 3.42m long when the rays of the sun are inclining at an angle of 40.5^o to the horizontal. What is the height of the pole?

 Give answer to 2 d.p.

X

(5) A boy X can be seen by two of his friends Y and Z, who are swimming in the sea.

40 m

      If the angle of elevation of X from Y is 23^o and from Z is 32^o, and the height of X

      above Y and Z is 40m. Calculate the horizontal distance:

      (i)  between X and Z.                     (ii) between X and Y              

      (iii) between Y and Z.

(6) A radio mast of 30m high is supported by two cables as shown.

      From the diagram:

        (i) find the distance between the two points A and B.

(1) The height of a tower is 15 m. A man looks at the tower from a distance of 120m. What is the angle of elevation of the top of the tower from man?
(2) Find the angle of depression ao of the structure.
(3) The height of a tree is 25 m. The shadow of the tree has a length of 30 m. Calculate the size of the angle marked po in the diagram
(4) A hot air balloon, M, is 900m vertically above a point N on the ground.      A boy stands at a point O, 1200m  horizontally from N.                  (a) Calculate the distance, OM, of the boy from the balloon.                  (b) Calculate the angle MON.
(5) A and B are two villages. If the horizontal distance between them is 12km and the vertical distance between them is 2 km, calculate:      (i) the shortest distance between the two villages,      (ii) the angle of elevation of B and A.
(6) A man at the top of a vertical cliff observes a boat (B) at sea. From the diagram,                 (i) State the angle of depression of the boat from the man.                 (ii) How far is the boat from the cliff?
(7) Two planes A and B are flying directly above each other. A person (P) can see both of them. The vertical height between B and P is 5 km. if the angles of elevation of the planes        from person are 65o and 75o, calculate:        (i) horizontal distance of P from the two planes.        (ii) the vertical distance between A and B.

(8) Two people A and B are standing either side of a transmission mast.

      A is 130m away from the mast and B is 200m away.

      If the angle of elevation of the top of the mast from A is 60^o.

      Calculate

     (i) the height of the mast

     (ii) the angle of elevation of the top of the mast from B.

 (9) A girl standing on a hill at A, overlooking a lake, can see a small boat at a point B on the lake.

 If the girl is at a height of 50m above B and at a horizontal

 distance of 120m away from B, calculate:

(i) the angle of depression of the boat from the girl,

(ii) the shortest distance between the girl and the boat.

# Note : Teachers are required to provide suitable diagrams for the questions