Question

The angle of elevation of top of the tower from a point on ground is 45 degrees. On walking 30m towards the tower, the angle of elevation becomes 60 degrees. Find height of the tower and its distance from the foot to the tower.​

Answer 1

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Answer 2

The height of the tower is approximately 51.96 meters and the distance from the foot of the tower to the point on the ground is approximately 85.98 meters.

Let the height of the tower be "h" and the distance from the foot of the tower to the point on the ground be "x".

We can use the tangent function to set up two equations involving "h" and "x".

From the first observation, we know that:

tan(45) = h/x

Simplifying this, we get:

h = x

From the second observation, we know that after walking 30m towards the tower, the angle of elevation is 60 degrees.

This means we have a right triangle with one leg of length "h" (the height of the tower), another leg of length "x-30" (the distance from the foot of the tower to the point on the ground after walking 30m), and a hypotenuse of length "x" (the original distance from the foot of the tower to the point on the ground).

Using the tangent function again, we can write:

tan(60) = h/(x-30)

Simplifying and substituting h = x from the first equation, we get:

$\sqrt{3} = x/(x-30)$

Multiplying both sides by (x-30) and simplifying, we get:

$x \sqrt{3} - 30\sqrt{3} = x$

Solving for x, we get:

$x = 30*\sqrt{3} + 1)$

Substituting this value of x into h = x, we get:

$h = 30*(\sqrt{3} ) + 1)$

Therefore, the height of the tower is approximately 51.96 meters and the distance from the foot of the tower to the point on the ground is approximately 85.98 meters.

For similar question on angle of elevation.

https://brainly.in/question/47120708

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