Ncert – Class 10 – Application of Trigonometry – Hots Question
Question 1
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
Solution
Height of the building = AZ = 30 m.
AB = AZ – BZ = 30 – 1.5 = 28.5
Measure of AB is 28.5 m
In right ΔABD,
tan 30° = AB/BD
1/√3 = 28.5/BD
BD = 28.5√3 m
Again,
In right ΔABC,
tan 60° = AB/BC
√3 = 28.5/BC
BC = 28.5/√3 = 28.5√3/3
Therefore, the length of BC is 28.5√3/3 m.
XY = CD = BD – BC = (28.5√3-28.5√3/3) = 28.5√3(1-1/3) = 28.5√3 × 2/3 =
57/√3 = 19√3 m.
Thus, the distance boy walked towards the building is 19√3 m.
Question 2
The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500√3m.find the speed of the plane in km/hr.
Solution
720km/h
Question 3
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.
Solution
40 m
Question 4
A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60° to 30°. Find the speed of the boat in metres per minute
Solution
The speed of boat is 57.74 m/min.
Question 5
A man standing on the deck of a ship, which is 10 m above the water level, 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 height of the hill
Solution
AD = AB + BD = 30 m + 10 m = 40 m
The distance of the hill from the ship is 17.3 m and the height of the hill is 40 m
Question 6
As observed from the top of a lighthouse , 75 m high 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 between the two ships
Solution
75(√3-1) m
Question 7
From a point on the ground, the angle ofelevation of the top of a tower isobserved to be 60° From a point 40 m vertically above the first point of observation, the angle of elevation of the top of the tower is 30°. Find the height of the tower and its horizontal distance from the point of observation.
Solution
Height of tower is 60m
Horizontal distance from point of observation is 20√3m
Question 8
A flag-staff stands at the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60°and from the same point, the angle of elevation of the top of the tower is 45°Find the height of the flag-staff.
Solution
Height of flag staff is 3.66m
Question 9
The angle of elevation of a jet plane from a point A on the ground is 60°. After a flight of 30
seconds,the angle of elevation changes from 60° to 30°.If the jet plane is plane is flying at a
constant height of 1200√3m,then find the speed of the jet plane
Solution
288 km/hr
Question 10
The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60°. Find the height of the cloud
Solution
height of cloud = AC
= (H + 60) m = (60 + 60) m = 120 m
