Advertisements
Advertisements
प्रश्न
In the given figure, AB is tower of height 50 m. A man standing on its top, observes two car on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the two cars.
उत्तर
Clearly ∠ADB = 45° and ∠ACB = 30° ....[∵ Angle of depression = Angle of elevation]
Now, In ΔABD, we have
tan 45° = `(AB)/(BD)`
⇒ 1 = `50/(BD)`
⇒ BD = 50 m ...(i)
Also, In ΔABC, we have
tan 30° = `(AB)/(BC)`
⇒ `1/sqrt(3) = (AB)/(BC)`
⇒ BC = `ABsqrt(3) = 50sqrt(3)` m ...(ii)
From equations (i) and (ii), we get
CD = BC + BD
= `(50sqrt(3) + 50)`m
= `50(sqrt(3) + 1)`m
= 50(1.732 + 1)
= 50 × 2.732
= 136.6 m
Thus, the distance between two cars is 136.6 m.
संबंधित प्रश्न
In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.
From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.
As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use `sqrt3` = 1.732]
A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.
The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiation control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms
A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is C to the North of B?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)
In given figure, the value of CE is ____________.
Two poles are 25 m and 15 m high, and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is ______.
There are two windows in a house. A window of the house is at a height of 1.5 m above the ground and the other window is 3 m vertically above the lower window. Ram and Shyam are sitting inside the two windows. At an instant, the angle of elevation of a balloon from these windows is observed as 45° and 30° respectively. Find the height of the balloon from the ground.
