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Lastlap2016
AC is the hypotenuse of the right angled triangle and AC=50. now slope of AC =4/3 i.e tan θ = 4/3 where θ = ∠ACE E is a point BC extended.

now since tan θ = 4/3 so sec θ = 5/3 using identity sec^2 + tan^2 =1

so cos θ= 3/5 and therefore sin θ= 4/5 and sin θ= sin(180- θ) so we get the ratio of AB/AC which is 4/5 and AC=50. So Ab=40.

Hi,
Trignometry is not tested on GMAT, so there would be another way of solving it..
slope is \(\frac{y}{x}= \frac{4}{3}\) .. this gives us the ratio of two sides..

let common terms be 'a', so one side = 4a and 2nd side = 3a..
Now AB is vertical side and BC is horizontal side .. so basically AB talks of move along y-axis..
sides are 3a:4a:50 clearly right angle triangle of 3:4:5..
so the sides become 30:40:50..
as AB is the longer side -- moving in Y-axis direction= AB = 40
E
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Attachment:
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abc.jpg [ 4.64 KiB | Viewed 1946 times ]

According the Pythagoras theorem, we get a^2+b^2=c^2. Normally, many problems involve 3^2+4^2=5^2. Hence, we can apply the rule to this question and get 30^2+40^2=50^2. Hence, the answer is 40 and the correct answer choice is E.
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In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 50 and the slope of line segment AC is 4/3, what is the length of AB?

A. 12
B. 18
C. 24
D. 28
E. 40

* A solution will be posted in two days.

@Moderators,

Please move this question to PS forum :)
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