Question 1: In the figure, given below, it is given that is perpendicular to and is of length meters. and Without using tables, find

Answer:

Substituting from above

Question 2: Find the height of a tree when it is found that on walking away from it ? in a horizontal line through its base, the elevation of its top changes to

Answer:

Substituting from above

Question 3: Find the height of a building, when it is found that on walking towards it in a horizontal line through its base the angular elevation of its top changes to

Answer:

Substituting from above

Question 4: From the top of a light house high, the angles of depression of two ships are observed as and respectively. Find the distance between the two ships (in the nearest meter) if:

(i) the ships are on the same side of the light house,

(ii) the ships are on the opposite sides of the light house. **[2010]**

Answer:

(i)

Therefore, the dis\tance between the ships is =

(ii) If the ships were on the opposite sides, then the distance between the ships is =

Question 5: Two pillars of equal heights stand on either side of a roadway, which is wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are and ; find the height position of the pillar and the position of the point.

Answer:

Hence

Question 6: From the figure, given below, calculate the length of

Answer:

Question 7: The angle of elevation of the top of a tower is observed to be At a Point, vertically above the first point of observation, the elevation is found to be Find: (i) the height of the tower, (ii) its horizontal distance from the points of Observation

Answer:

Given

Question 8: From the top of a cliff, high, the angles of depression of the top and bottom of a tower are observed to be and Find the height of the tower.

Answer:

Question 9: A man on a cliff observes a boat. at an angle of depression , which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be Assuming that the boat sails at a uniform speed, determine: (i) how much more time it will take to reach the shore. (ii) the speed of the boat in meter per second if the height of the cliff is

Answer:

Also

Therefore the time that the boat will take to reach the shore

Speed of the boat

Question 10: A man in a boat rowing away from a lighthouse high, takes minutes to change the angle of elevation of the top of the lighthouse to Find the speed of the boat.

Answer:

Question 11: A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is When he moves away from the bank, he finds the angle of elevation to be Find: (i) the height of the free, correct to decimals places, (ii) the width of the river.

Answer:

Question 12: The horizontal distance between two towers is and the angular depression of the top of the first tower as seen from the top of the second. which is high, is Find the height of the first tower.

Answer:

Question 13: The length of the shadow of a tower standing on level plane is found to be meters longer when the sun’s altitude is then when it is Prove that the height of the tower is meters.

Answer:

Multiplying both numerator and denominator by we get

Question 14: After seconds, its elevation is observed to be ; find the uniform speed of the Aeroplane in km per hour.

Answer:

Question 15: From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be and respectively. Find the distances of the two stones from the foot of the hill. **[2007]**

Answer: