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In x-y plane, there is a right triangle ABC (∠B=90o). If the length o

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In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   02 May 2016, 21:20
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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.
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E
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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   02 May 2016, 22:33
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.
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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   02 May 2016, 22:49
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Slope = Change in Vertical Direction/Change in Horizontal Direction = 4/3

Change in Vertical Direction = 4x = AB
Change in Horizontal Direction = 3x = BC

AB^2 + BC^2 = 50^2

16x^2 + 9x^2 = 2500

25x^2 = 2500

x^2 = 100

x = 10

Therefore AB = 10*4 = 40

Answer: E
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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   02 May 2016, 23:02
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Lastlap2016 wrote:
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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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   15 May 2016, 06:13
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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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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   09 Jul 2016, 10:07
MathRevolution wrote:
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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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink] New post   21 Apr 2020, 05:21
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Re: In x-y plane, there is a right triangle ABC (∠B=90o). If the length o [#permalink]
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