Question 1: Find :

Answer:

Question 2: In the following diagram, is a floor-board; is a cubical box with each edge and . Calculate the length of the board .

Answer:

Question 3: Calculate .

Answer:

Question 4: Calculate .

Answer:

Question 5: The radius of a circle is given as and chord subtends an angle of at the center of the circle. Using trigonometry, calculate: (i) the length of ; (ii) the distance of from the center .

Answer:

Therefore

Question 6: At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is on walking meters towards the tower; the tangent of the angle is found to be Find the height of the tower.

Answer:

Therefore

Hence

Question 7: A vertical tower stands on horizontal plane and is surmounted by a vertical flagstaff of height meter. At a point on the plane, the angle of elevation of the bottom of the flagstaff is and that of the top of flagstaff is . Prove that the height of the tower is .

Answer:

Question 8: 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 meters from the pole. Give your answer to the nearest degree. **[1999]**

Answer:

m

i) m

ii) if the distance from pole m

Question 9: The angles of elevation of the top of a tower from two points on the ground at distances and meters from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is meter.

Answer:

Question 10: 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 11: A vertical tower is high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is . How far is he standing from the foot of the tower?

Answer:

Question 12: 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 13: A high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower, as seen from the foot of the pole, is and angle of elevation of the top of the pole as seen from the foot of the tower is . Find: (i) the height of the tower (ii) the horizontal distance between the pole and the tower.

Answer:

Question 14: A vertical pole and vertical tower are on the same ground level ground in such a way that from the top of the pole the angle of elevation of the top of the tower is and the angle of depression of the bottom of the tower is Find: (i) the height of the tower, if the height of the pole is ;(ii)the height of the pole; if the height of the tower is .

Answer:

i)

m

Height of tower m

ii)

m

Question 15: From a point, above the surface of a lake, the angle of elevation of a bird is observed to be and angle of depression of its image in the water of the lake is observed to be . Find the actual height of the bird above the surface of the lake.

Answer:

Now,

m

Therefore height of the bird m

Question 16: A man observes the angle of elevation of the top of a building to be . He walks towards it in a horizontal line through its base. On covering , the angle of elevation changes to . Find the height of the building correct to the nearest meter.

Answer:

m m

Question 17: As observed from the top of a, tall lighthouse, the angles of depression of two ships, on the same side of the light house 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:

m m

Question 18: In the given figure, from the top of a building high, the angles of depression of the top and bottom of a vertical lamp post are observed to be and respectively. Find: (i) the horizontal distance between and . (ii) the height of the lamp Post.

Answer:

i) m

ii) m

Question 19: 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:

m

Therefore the width of the river

m