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In the given figure, ABC is right-angled triangle, right-angled at B. 04 Jul 2021, 02:26
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75% (hard)

Question Stats:

58% (02:46) correct 42% (02:46) wrong based on 185 sessions

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In the given figure, ABC is right-angled triangle, right-angled at B. If angle BAC = 30° what is the y-coordinate of B?

A. \( 2\sqrt{}3\)
B. \( 4\sqrt{}3\)
C. \(2+2\sqrt{}3\)
D. \(4+\sqrt{}3\)
E. None of the above
​
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D
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In the given figure, ABC is right-angled triangle, right-angled at B. 04 Jul 2021, 10:03
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junii

In the given figure, ABC is right-angled triangle, right-angled at B. If angle BAC = 30° what is the y-coordinate of B?

A. \( 2\sqrt{}3\)
B. \( 4\sqrt{}3\)
C. \(2+2\sqrt{}3\)
D. \(4+\sqrt{}3\)
E. None of the above
​
Show Spoiler
Attachment:
The attachment geometry.PNG is no longer available

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Draw a perpendicular from B that meets AC at D.

Two ways.

I. Visual
Line AC is 4 from x axis, so y-coordinates of B will be 4+length of AD.
Only D is in that format. In all probability, D should be the answer.

II. 30-60-90
ABC is 30-60-90 and AC is 7-3=4.
Thus, AB opposite \(60^o\) will be \(4*\sqrt{3}/2=2\sqrt{3}\)

Now ABD is also 30-60-90 so sides will be in ratio \(1:\sqrt{3:2}\).
Thus BD opposite \(30^o\) will be \(2\sqrt{3}/2=\sqrt{3}\)

Y-Coordinate of B = 4+\(\sqrt{3}\)


D
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In the given figure, ABC is right-angled triangle, right-angled at B. 04 Jul 2021, 13:14
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chetan2u
junii

In the given figure, ABC is right-angled triangle, right-angled at B. If angle BAC = 30° what is the y-coordinate of B?

A. \( 2\sqrt{}3\)
B. \( 4\sqrt{}3\)
C. \(2+2\sqrt{}3\)
D. \(4+\sqrt{}3\)
E. None of the above
​
Show Spoiler
Attachment:
geometry.PNG



Draw a perpendicular from B that meets AC at D.

Two ways.

I. Visual
Line AC is 4 from x axis, so y-coordinates of B will be 4+length of AD.
Only D is in that format. In all probability, D should be the answer.

II. 30-60-90
ABC is 30-60-90 and AC is 7-3=4.
Thus, AB opposite \(60^o\) will be \(4*\sqrt{3}/2=2\sqrt{3}\)

Now ABD is also 30-60-90 so sides will be in ratio \(1:\sqrt{3:2}\).
Thus BD opposite \(30^o\) will be \(2\sqrt{3}/2=\sqrt{3}\)

Y-Coordinate of B = 4+\(\sqrt{3}\)


D
Show more

chetan2u
In the below statement of yours, i think u meant 4 + length of BD
"Line AC is 4 from x axis, so y-coordinates of B will be 4+length of AD."
Also, option B & C may not be in the format of "4 + something", but their values are more than 4.
Option B - 4 * sqrt(3) = 6.8
Option C - 2 + 2 sqrt(3) = 2 + 3.4 = 5.4

So, if we see at the values of option b & c, they also seem to be good candidate for answer. Request your comment.
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In the given figure, ABC is right-angled triangle, right-angled at B. 04 Jul 2021, 19:47
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pandajee
chetan2u
junii

In the given figure, ABC is right-angled triangle, right-angled at B. If angle BAC = 30° what is the y-coordinate of B?

A. \( 2\sqrt{}3\)
B. \( 4\sqrt{}3\)
C. \(2+2\sqrt{}3\)
D. \(4+\sqrt{}3\)
E. None of the above
​
Show Spoiler
Attachment:
geometry.PNG



Draw a perpendicular from B that meets AC at D.

Two ways.

I. Visual
Line AC is 4 from x axis, so y-coordinates of B will be 4+length of AD.
Only D is in that format. In all probability, D should be the answer.

II. 30-60-90
ABC is 30-60-90 and AC is 7-3=4.
Thus, AB opposite \(60^o\) will be \(4*\sqrt{3}/2=2\sqrt{3}\)

Now ABD is also 30-60-90 so sides will be in ratio \(1:\sqrt{3:2}\).
Thus BD opposite \(30^o\) will be \(2\sqrt{3}/2=\sqrt{3}\)

Y-Coordinate of B = 4+\(\sqrt{3}\)


D

chetan2u
In the below statement of yours, i think u meant 4 + length of BD
"Line AC is 4 from x axis, so y-coordinates of B will be 4+length of AD."
Also, option B & C may not be in the format of "4 + something", but their values are more than 4.
Option B - 4 * sqrt(3) = 6.8
Option C - 2 + 2 sqrt(3) = 2 + 3.4 = 5.4

So, if we see at the values of option b & c, they also seem to be good candidate for answer. Request your comment.
Show more

Hi, thanks. It is BD and a typo.

Now yes answer can be any of the B, C, D and E.

What would be BD in each case.
In B, 4+x=4\(\sqrt{3}……x=4(\sqrt{3}-1)\)
In C, x=\(2\sqrt{3}-2\)
And in D, \(x=\sqrt{3}\)

BD is opposite 30 degree angle. Which value of x fits in properly. It is \(\sqrt{3}\).
So, I meant that chances are high that it is D.
That was if you are in a hurry and do not have a clue on how to proceed.
But the proper method gives you the exact answer.
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In the given figure, ABC is right-angled triangle, right-angled at B. 26 Feb 2026, 09:43
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From the diagram we can find that ac= 4
Sin ø =1/2 = BC /ac = bc/4
So, bc=2
Draw a perpendicular from B to AC and name the point intersect as D.
Again, sin ø= 1/2 = BD/2✓3
So, bd= ✓3
Finally, distance of B from x-axis is bd+ 4 = 4 +✓ 3
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In the given figure, ABC is right-angled triangle, right-angled at B. 10 Mar 2026, 10:13
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Is this relevant for GMAT focus edition?
junii

In the given figure, ABC is right-angled triangle, right-angled at B. If angle BAC = 30° what is the y-coordinate of B?

A. \( 2\sqrt{}3\)
B. \( 4\sqrt{}3\)
C. \(2+2\sqrt{}3\)
D. \(4+\sqrt{}3\)
E. None of the above

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geometry.PNG

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In the given figure, ABC is right-angled triangle, right-angled at B. 10 Mar 2026, 10:16
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Is this relevant for GMAT focus edition?

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