A certain 13m ladder is resting against a wall of height X

Question

A certain 13m ladder is resting against a wall of height X at K degree with base. What is the height of the wall.

1) The angle between the base and the ladder is same as the angle between line 12x-5y = 10 and x axis. 
2) Distance between the base of the ladder and base of the wall is 5m.

There is no OA for this. This Q has been asked by a friend of mine who just appeared for the GMAT a day back.

As for me, I don't think with the mathematicals tools available for GMAT, we can find the degree that ladder is making with the base. Obv second stmt is an easy one. 
I would go with B for this.

Enlightenment guys..

hsourabh · Answer

If we apply the rules of trigonometry then I think even 1 is sufficient to answer the question. 
- From the equation of line, we can get the gradient (or inclination w.r.t X axis), which also means tangent of the angle. Therefore we can get the angle K in degrees.
- If we consider the premise, then sineK = X/13, K is known and hence X can be calculated.

2 is also sufficient to answer the question. So my choice is D.

Cheers,
Sourabh

ichha148 · Answer

humm , B is obvious

for A - if the angle between line 12x-5y = 10 and x axis is 45 or 60 degree then this will make either a 30-60-90 triangle or 45-45-90 and height can be easily determined

however i am not able to find a short way to figure out angle between 12x-5y and x-axis , so , can not comment

rathoreaditya81 · Answer

Same case with me. Can't seems to find any obvious and easy way to find the angle.

hSourabh, 
You sure that GMAT expects the candidate to know trignometry or even the basic rules of it for that sake?
Well, I am not sure and also I have never seen or heard any Q on gmat that expects any knowledge of trignometry.

Anyways, I am also not too sure how will you deduce the degree from the gradient? Though my knowledge of trigo has become very rusty but if I am not too wrong there used to be a conversion table to convert from some value to degree. Correct me if Iam wrong and do let me how you would find the degree.

GMAT TIGER · Answer

1: 12x-5y = 10
y = 12x/5 - 2

If x = 0, y = -2
If y = 0, x = 5/6

Since points (0, 0), (5/6, 0) and (0, -2) form a right angle triangle, the degree measure of the line 12x-5y = 10 and x axis is possible to know. Then, it is again possible to get the hight of the wall from the right angle triangle formed by the wall and the ladder that is lying on the wall.

(However it is even not necessary to do any calculation if we know that the info in statement 1 is sufficient to get the degree of the angle).

2: It is too easy for get the desired value. SUFF.

So D.

oracle · Answer

Both the conditions are sufficient. 
1) we know that the slope of the line from the given equation which is 12/5 since: 
y= (12/5)x-2

Now, slope of the line is Tan of the base angle. And Tan of angle (lets say angle A) for a right angled triangle is
TanA= opposite side/ adjacent side.

Lets say the base is z, 
x(height)/z(base) = 12/5

therefore, z= 5/12 x

Now, 
13^2 (hypotenuse)=x^2 + (5/12 x)^2

solving this we get x=12, hence suff.

2) when we know the base as 5 m 
we can compute x using the pythagorus theorem.

amittilak · Answer

I got choice D as well. 
For S2 It was simple enough to plot it and get the height. But I like the use of slope, & plugging it back in the pythagoras theorem. tht culd have saved me abt 30 secs. good job there buddy!

janani · Answer

i agree; answer is D

Pipp · Answer

If I assume that the wall is perpendicular to the base, then D is the answer. But I learned not to assume anything in GMAT, so unless it is stated explicitly that the wall is perpendicular to the base, I would go for E.

ulm · Answer

(D)
from (1) we have tg K = 12/5
we can calculate K and solve.
from (2) we have sqrt(169-25)=12 the same.

IanStewart · Answer

The wording of the question is a bit odd, since the line 12x-5y=10 forms two different angles with the x-axis, one acute, one obtuse. The question would need to make clear what angle is meant - I assume they mean the acute angle. The question should also surely make clear that the wall is perpendicular to the ground; without these clarifications the answer would be E, but it would also be a pretty boring question.

You don't need trigonometry here, since we don't actually care what the angles are. If Statement 1 is true, then the triangle made by the line 12x-5y = 10, the x-axis and the y-axis is *similar* to the triangle made by the ladder, the ground and the wall, since the angles are the same in each triangle. Now, if we wanted to, we could find the lengths of all of the sides of our triangle in the coordinate plane. We'd then have two similar triangles, and we'd know all of the lengths in one triangle, and one length in the other. So using similarity we could find all of our lengths, and in particular, the height of the wall. Since it's a DS question, obviously we don't want to actually solve anything. Since Statement 2 is sufficient, the answer is D.

itsnotover · Answer

Great Question!
I thought B is only suff.
After going through the posts convinced with D (both are suff.)
Thanks for posting!

jatt86 · Answer

ans should be d

coz if we know any side + degree measure then we can fing all sides in right angled triangle( this could be some sort of rule )

raajarshi · Answer

Sorry if my understanding is wrong, but it is my first attempt, please be kind.
Should we assume that the ladder comes to the top of the wall? If that is the case, it is a plain question and either of (A) or (B) suffice to find the answer, but if it is not said that the ladder comes to the top of the wall, it is not possible to answer the question. In my opinion, the question just says, it is resting against the wall, so we cannot determine the height of the wall.

magnetictempest · Answer

Statement 1: Sufficient
You can resolve K into slope of 12/5 which has been mentioned earlier, and when used as the height & distance from base conveniently makes a right triangle with the 13 ladder

Statement 2: Sufficient
You can make a special triangle 5 from base with the 13 hypotenuse to make a right triangle.

Either/Or.
Both good.
D

KarishmaB · Answer

Responding to a pm:

As the question stands, the answer is (E). Clarifying that the wall is perpendicular is one reason but more importantly, nothing says that the top of the ladder rests against the top of the wall. The ladder could very well be placed such that there is quite a bit of the wall above the top of the ladder or such that the top of the ladder is in the air due to a shorter wall. If you have done trigonometry questions before, you would know that the wall being taller is a scenario faced quite often and hence it is an easy (E). Since there is no way to calculate how much wall is above the ladder, there is no way to get the height of the wall.

But assuming that the actual question clarified all these issues, both statements independently would be sufficient to answer the question.

Pythagorean theorem helps you establish that statement 2 is sufficient alone.

As for statement 1, there are many ways of establishing that it is sufficient alone. Without using any trigonometry, I would think of an infinite base and infinite wall. 
12x-5y = 10 gives us the slope of the ladder (y = (12/5)x - 2) so slope is 12/5. This is the slope of the ladder. We hold a line at the point where the base and wall meet and start moving it outward. We need to maintain the slope of 12/5. We keep moving it away from the point and at only one place will the length between the base and the wall be 13. Hence the wall will have a fixed length.

Using trigonometry, we know that the slope is 12/5 which is TanQ which gives us Q. Since we have the length of the hypotenuse, using SinQ, we can get the length of the wall.

Answer (D)

kundankshrivastava · Answer

A triangle can be uniquely drawn if following is given :
1. three sides
2. Two sides and one angle
3. one side and two angles

In this problem, height of ladder (one side) and angle of wall to the base i.e 90 deg (one angle) is given.

First condition will give another angle and as per No 3 the triangle can be uniquely drawn (one side and two angle)

Second condition will give another side and as per No 2 the triangle can be uniquely drawn (two side and one angle)

From the above , it is clear that both are individually sufficient to draw the triangle and then height of wall can be determined. Hence D is the answer

A certain 13m ladder is resting against a wall of height X

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A certain 13m ladder is resting against a wall of height X

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