Let's do this question.
A car is moving towards a huge building at that point, the angle of elevation from the car to the top
of the house is 30 degrees.
After moving a hundred meters towards the building, the angle of elevation is 45 degree.
Find the height of the building.
OK, so give it a try and then we'll do it together.
And do remember to always start withdrawing the sketch of this question before you start attempting
it.
OK, so we are back.
I hope you have given it a try.
Let's draw the sketch of this question first.
So it's given that a car is moving towards the building and at a point the angle of elevation from the
car to the top of the house is 30 degree.
This angle over here is 30 degrees.
Now, after some time, the car has moved hundred meters towards the building and the new angle of elevation
is forty five degrees.
So let's draw it like this.
This angle is 45 degrees and this distance over here is a meters.
Now we need to find the height of the building.
That is, we need to find the value of X.
Let this be white.
All right.
Let's start finding the tan value of 30 degrees.
So Tan 30 is opposite by adjacent, right?
So Tan 30 is equal to X by one hundred plus white.
And we know that the value of tan that is equal to one by road trip.
OK, so X by 100 plus Y is equal to one barratry.
Now let's cross multiply and we get three, X is equal to hundred plus.
Right right now let's take ten forty five thousand forty five X divided by Y.
Right because standard is opposite by Addison Houtan forty five is X Y and we know that the value of
ten forty five is equal to one.
So we write that equal to one and X is equal to Y over here right now.
Let's substitute it over here now putting in sort of white let me put X so this becomes rule three plus
one that is equal to one hundred plus X.
Now on solving I get X in the room, three minus one is equal, two hundred or X is equal to under divided
by rule three minus one.
Now that is the answer, that's the height of the building.
But you will observe that there is no such option given.
Right.
There is no such option given.
So what you need to do is you need to rationalize the denominator.
Let me write that over here.
You need to rationalize.
The denominator.
What does that mean?
Well, I hear you have a root three, right, so basically you need to remove this root tree.
That's what we call rationalizing the denominator.
Now, we use a property for this.
We know that A minus B into A plus B is equal to a square, minus B square.
Now, let's apply this formula to rationalize the denominator.
So over here, I have under divided by rule three, minus one right now.
Let's multiply both the numerator and denominator with root three plus one.
So I have what we are all three minus one.
So I multiply the numerator and denominator with three plus one and let's simplify the numerator becomes
100 in the root three plus one.
But over here you have A minus B into A plus B, that's equal to A square minus B square.
Right.
That will become root three square which is three minus one square which is one, two, three, minus
one is equal to two.
So this simplifies two hundred root three plus one divided by two and that's equal to 50 in to rule
three plus one.
That is option E over here and therefore is the correct answer to this question.