An aeroplane flying horizontally 1km above the ground is observed at an elevation of 60degree. After a flight of 10 seconds it's angle of elevation is observed to be 30 degree from the same point on he ground. Find the speed of the aeroplane in km/hour

tan 60 = X1/1

tan 30 = X2/1

d = X2 - X1

v = d/t

t in hours = 10 s /(3600 s/hour)

To solve this problem, we can use trigonometry and the concept of right triangles. Let's break down the given information:

- The aeroplane is flying 1 km above the ground.
- The initial angle of elevation is 60 degrees.
- After a flight of 10 seconds, the angle of elevation is now 30 degrees.

We can start by drawing a diagram to better understand the situation.

In the diagram, let's label the following:
- AB represents the initial position of the aeroplane.
- AC represents the final position of the aeroplane after the flight.
- BD represents the altitude of the aeroplane (1 km).

A
|\
| \
B D
| \
|___C

Now, let's analyze the right triangle ABC. We know that BD is perpendicular to AC, so triangle ABC is a right triangle.

Using trigonometry, we can determine the lengths of the sides of the triangle.

Let x be the distance covered in 10 seconds. We can find x using the equation: x = speed * time.
Since we want to find the speed in km/hour, we need to convert 10 seconds to hours. 1 hour is equal to 3600 seconds, so 10 seconds is equal to 10/3600 hours.

Now, let's calculate the value of x:
x = speed * (10/3600)

From the right triangle ABC, we can use the tangent function to find the value of x. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

tan(60 degrees) = (AB + BD) / x
tan(30 degrees) = BD / x

Substituting the values of the angles and lengths into the equations, we get:

tan(60 degrees) = (AB + 1) / x
tan(30 degrees) = 1 / x

Now, let's solve for x:

tan(60 degrees) = (AB + 1) / (speed * (10/3600))
tan(30 degrees) = 1 / (speed * (10/3600))

We can now calculate the values of tan(60 degrees) and tan(30 degrees) using a calculator:

tan(60 degrees) ≈ 1.732
tan(30 degrees) ≈ 0.577

Substituting the values in the equations, we get:

1.732 = (AB + 1) / (speed * (10/3600))
0.577 = 1 / (speed * (10/3600))

Let's solve these equations:

1.732 = (AB + 1) / (speed * (10/3600))
Multiply both sides by speed * (10/3600):
1.732 * speed * (10/3600) = AB + 1
Divide both sides by 1.732 * (10/3600):
(speed * 10) / (1.732 * 360) = AB + 1

0.577 = 1 / (speed * (10/3600))
Multiply both sides by speed * (10/3600):
0.577 * speed * (10/3600) = 1
Divide both sides by 0.577 * (10/3600):
(speed * 10) / (0.577 * 360) = 1

Simplifying the equations further:
(speed * 10) / (627.96) = AB + 1

(speed * 10) / (206.398) = 1

Now, we can solve for the value of speed:

(speed * 10) = (206.398)
Divide both sides by 10:
speed = 206.398 / 10

Therefore, the speed of the aeroplane is approximately 20.64 km/hour.