Data Suff: Sides of a Triangle. CAT Exam #2

[afvatcha]

I posted the entire problem below. I felt that either answer should be sufficient. If you have a large triangle and within that triangle you know for a fact that one of the two smaller triangles in a 30-60-90, why can't you assume the other smaller triangle is a 30-60-90?

The correct answer was C.

If AD is 6, and ADC is a right angle, what is the area of triangular region ABC?

(1) Angle ABD = 60°

(2) AC = 12

[afvatcha]

I have attached a pic via link below.

http://www.postimage.org/image.php?v=gx1cJ7ui

[jchong8250]

I think the main thing to take away here is that although the drawing makes it seem like the triangle can be an isosceles, you can't assume that. In (A), you can figure out the length of BD using the 30-60-90 triangle properties, but you can't assume the same properties for triangle ADC. For (B), you can figure out the length of DC using the Pythagorean Theorem. So, you'd need both (A) and (B) to figure out the area of triangle ABC.

[afvatcha]

Thanks. I knew that if there are two 30-60-90 triangles within a larger triangle then you know the larger triangle is an equaliteral triange. But you cannot assume that if one of the smaller triangles is a 30-60-90 then the other has to be a 30-60-90. Thanks again.

[Ben Ku]

jchong8250: good points.

Key takeaway is that pictures can be deceiving. Solve problems only with information that has been explicitly stated.

[ganeshraj]

Cannot we solve the problem with (A) alone,

In triangle ABD , we know : AD=6 ,and B=60 dg.

tan x = opp/adj (x = B )
=> tan 60 = 6/BD.
=> sqrt 3 = 6 /BD.
=> BD = 2 sqrt 3.

Area of the triangle ABD = 1/2 .6. 2 sqrt 3 =>6 sqrt 3.

[ganeshraj]

Sorry , got the question wrong; its area of triangle ABC ,not ABD.

Thanks.

[RonPurewal]

Cannot we solve the problem with (A) alone,

In triangle ABD , we know : AD=6 ,and B=60 dg.

tan x = opp/adj (x = B )
=> tan 60 = 6/BD.
=> sqrt 3 = 6 /BD.
=> BD = 2 sqrt 3.

Area of the triangle ABD = 1/2 .6. 2 sqrt 3 =>6 sqrt 3.

fyi, you should make sure that you have the skill set to solve 30°-60°-90° triangles without trigonometry. i.e., you should just memorize the ratio of the sides (1:√3:2), so that you don't have to waste precious time setting up trig functions.

...especially since trigonometry is not required on this test!

the only right triangles for which you'll have to determine side lengths are 30-60-90, 45-45-90, and/or triangles for which the pythagorean theorem is all you need.