Advertisements
Advertisements
Question
The angles of depression of two cars on a straight road as observed from the top of a 42m high building are 60° and 75° respectively. Find the distance between the cars if they are on opposite sides of the building.
Solution
Let the position of the two cars be A and C. Let BO be the building of height 42 m.
In ΔBAD,
`tan75^circ = "BD"/"AD"`
⇒ `3.7321 = 42/"AD"`
⇒ `"AD" = 42/3.7321`
⇒ AD = 11.25 ....(1)
In ΔBDC,
`tan60^circ = "BD"/"DC"`
⇒ `sqrt(3) = 42/"DC"`
⇒ `"DC" = 42/1.732 = 24.25` ....(2)
∴ AC = AD+ DC = 11.25 m + 24.25 m = 35.5 m
Thus, the distance between the cars is 67.63 m.
APPEARS IN
RELATED QUESTIONS
The angle of elevation of the top of a tower, from a point on the ground and at a distance of 160 m from its foot, is found to be 60°. Find the height of the tower.
Two climbers are at points A and B on a vertical cliff face. To an observer C, 40 m from the foot of the cliff, on the level ground, A is at an elevation of 48° and B of 57°. What is the distance between the climbers?
The angle of elevation of the top of a tower is observed to be 60°. At a point, 30 m vertically above the first point of observation, the elevation is found to be 45°. Find:
- the height of the tower,
- its horizontal distance from the points of observation.
A vertical tower is 20 m 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 0.53. How far is he standing from the foot of the tower?
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:
- the height of the tower;
- the horizontal distance between the pole and the tower.
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. If the boats are on the opposite sides of the aeroplane, find the width of the river. Write the answer correct to the nearest whole number.
The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string Is 200m and it makes an angle of 45° with the ground. Find the distance of the pole to which the string is tied from the base of the tree.
An observer, 1.5m tall, is 28.5m away from a tower 30m high. Determine the angle of elevation of the top of the tower from his eye.
A man standing on a cliff observes a ship at an angle of depression of the ship is 30°, approaching the shore just beneath him. Three minutes later, the angle of depression of the ship is 60°. How soon will it reach the shore?
The string of a kite is 150 m long and it makes an angle of 60° with the horizontal. Find the height of the kite from the ground.
