Question 1: With reference to the given figure of a man stands on the ground at point , which is on the same horizontal plane as , the foot of the vertical pole . The height of the pole is . The man’s eye is above the ground. He observes the angle of elevation of , the top of the pole, as where Calculate: (i) the distance in meters; (ii) angle of elevation of the top of the pole when he is standing eters from the pole. Give your answer to the nearest degree. **[1999]**

Answer:

i)

ii) if the distance from pole

Question 2: From a window , above the ground the angle of elevation of the top of a tower is , where and the angle of depression of the foot of the tower is where . See the given figure. Calculate the height of the tower in meters. **[2000]**

Answer:

Question 3: A man standing on the bank of a river observes that the angle of elevation of the top of the tower is . When he moves away from the bank. he finds the angle of elevation to be . Calculate: (i) the width of the river and (ii) the height of the tree. **[2003]**

Answer:

Let the height of the tree

Let the width of the river

Question 4: As observed from the top of a, tall lighthouse, the angles of depression of two ships, on the same side of the lighthouse in horizontal line with its base, are and respectively. Find the distance between the two ships. Give your answer correct to the nearest meter. **[2012]**

Answer:

Question 5: An airplane, at an altitude of observes the angles of depression of two boats on the opposite banks of a river to be and respectively. Find the width of the river. Write the answer correct to the nearest whole number. **[2014]**

Answer:

Therefore the width of the river

Question 6: 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) From

Similarly, from

Therefore, the dis\tance between the ships is =

(ii) If the ships were on the opposite sides, then the dis\tance between the ships is =

Question 7: 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:

From

Similarly, from

Therefore