A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is 45° and the angle of depression of the base is 30°. Calculate he distance of the cliff from the ship and the height of the cliff.
A man standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill'as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
HEIGHTS AND DISTANCES | ICSE CLASS 10 CHAPTER 22 | EX 22 B | EX 22C | SELINA SOLUTIONS
EXERCISE 22B
10. A man in a boat rowing away from a lighthouse
150 m high, takes 2 minutes to change the angle of elevation of the top
of the lighthouse from 60° to 45°. Find the speed of the boat.
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 60°.
When he moves 40 m away from the bank, he finds the angle of elevation
to be 300. Find : (i) the height of the tree, correct to 2 decimal
places, (ii) the width of the river.
12. The horizontal
distance between two towers is 75 m and the angular depression of the
top of the first tower as seen from the top of the second, which is 160 m
high, is 45°. Find the height of the first tower.
EXERCISE 22C
9. The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is
10. From a window A, 10 in above the ground the angle of elevation of the top C of a 5 tower is x°, where tan x° the angle of depression of the foot D of the tower is y°, where 1 tan y° = 4. (See the given figure). Calculate the height CD of the tower in metres.
12. A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate : (i) the width of the river and (ii) the height of the tree.
13. A 20 m 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 60° and the angle of elevation of the top of the pole as seen from the foot of the tower is 30°. Find : (i) the height of the tower. (ii) the horizontal distance between the pole and the tower.
19. An aeroplane, at an altitude of 250 m, observes the angles of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. Find the width of the river. Write the answer correct to the nearest whole number.
