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Let's do this question.

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A car is moving towards a huge building at that point, the angle of elevation from the car to the top

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of the house is 30 degrees.

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After moving a hundred meters towards the building, the angle of elevation is 45 degree.

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Find the height of the building.

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OK, so give it a try and then we'll do it together.

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And do remember to always start withdrawing the sketch of this question before you start attempting

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it.

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OK, so we are back.

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I hope you have given it a try.

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Let's draw the sketch of this question first.

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So it's given that a car is moving towards the building and at a point the angle of elevation from the

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car to the top of the house is 30 degree.

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This angle over here is 30 degrees.

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Now, after some time, the car has moved hundred meters towards the building and the new angle of elevation

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is forty five degrees.

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So let's draw it like this.

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This angle is 45 degrees and this distance over here is a meters.

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Now we need to find the height of the building.

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That is, we need to find the value of X.

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Let this be white.

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All right.

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Let's start finding the tan value of 30 degrees.

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So Tan 30 is opposite by adjacent, right?

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So Tan 30 is equal to X by one hundred plus white.

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And we know that the value of tan that is equal to one by road trip.

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OK, so X by 100 plus Y is equal to one barratry.

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Now let's cross multiply and we get three, X is equal to hundred plus.

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Right right now let's take ten forty five thousand forty five X divided by Y.

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Right because standard is opposite by Addison Houtan forty five is X Y and we know that the value of

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ten forty five is equal to one.

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So we write that equal to one and X is equal to Y over here right now.

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Let's substitute it over here now putting in sort of white let me put X so this becomes rule three plus

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one that is equal to one hundred plus X.

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Now on solving I get X in the room, three minus one is equal, two hundred or X is equal to under divided

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by rule three minus one.

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Now that is the answer, that's the height of the building.

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But you will observe that there is no such option given.

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Right.

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There is no such option given.

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So what you need to do is you need to rationalize the denominator.

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Let me write that over here.

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You need to rationalize.

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The denominator.

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What does that mean?

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Well, I hear you have a root three, right, so basically you need to remove this root tree.

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That's what we call rationalizing the denominator.

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Now, we use a property for this.

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We know that A minus B into A plus B is equal to a square, minus B square.

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Now, let's apply this formula to rationalize the denominator.

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So over here, I have under divided by rule three, minus one right now.

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Let's multiply both the numerator and denominator with root three plus one.

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So I have what we are all three minus one.

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So I multiply the numerator and denominator with three plus one and let's simplify the numerator becomes

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100 in the root three plus one.

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But over here you have A minus B into A plus B, that's equal to A square minus B square.

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Right.

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That will become root three square which is three minus one square which is one, two, three, minus

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one is equal to two.

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So this simplifies two hundred root three plus one divided by two and that's equal to 50 in to rule

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three plus one.

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That is option E over here and therefore is the correct answer to this question.