didieravoaka wrote:In triangle ABC, angle A and angle B are 30 and 60 degrees respectively. What is the length of the side opposite angle C?

(1) The side opposite angle B has length 4.

(2) The side opposite angle C is twice the length of the side opposite angle A.

The total of the measures of the angles of a triangle is 180 degrees. So if two angles of that triangle measure 30 and 60 degrees, then the third angle measures 90 degrees and the triangle is a 30 - 60 - 90 triangle.

The two sides and hypotenuse of a 30 - 60 - 90 triangle are always in the proportion 1:√3:2 respectively.

Since angle C is 90 degrees, then the side opposite angle C is the hypotenuse. So this question is asking for the length of the hypotenuse of a 30 - 60 - 90 triangle.

Statement 1:

The question tells us that angle B is 60 degrees. Since angle B is larger the two angles opposite a non hypotenuse side of the triangle, we know that the side opposite B is the longer of the two non hypotenuse sides of the triangle and that the ratio of the length of B to the hypotenuse is the following.

√3:2

So since we have the length of B, we can calculate the length of the hypotenuse.

Sufficient.

Statement 2:

It is the case for every 30 - 60 - 90 triangle that the hypotenuse is twice as long as the side opposite the 30 degree angle. So without additional information there is no way to calculate the length of the hypotenuse.

Insufficient.

The correct answer is A.

Are there some logical math to solve this question ? Because I am still confused

John fran kennedi wrote:Are there some logical math to solve this question ? Because I am still confused

Hi. At which point do you get confused? Here is an image of the situation.

Hi Marty,

I thought measures of 30-60-90 triangle were such that short-long-hypotenuse. My understanding was that angles would be the way around if I'm referring to your picture.

So, is that false to think that 30-60-90 triangle as such that they are short-long-hypotenuse?

Thanks Marty!

didieravoaka wrote:Hi Marty,

I thought measures of 30-60-90 triangle were such that short-long-hypotenuse. My understanding was that angles would be the way around if I'm referring to your picture.

So, is that false to think that 30-60-90 triangle as such that they are short-long-hypotenuse?

Thanks Marty!

The 30 angle is opposite the shorter side. The 60 angle is opposite the longer side. The 90 degree angle is opposite the hypotenuse.

It makes sense that the shorter side would be opposite the smaller angle, right?

The triangle in the image is correctly drawn.

Yes Marty, It makes sense.

I was not arguing about the image I was trying to understand. And Thanks again!

Now, I can clearly see that triangle 45-45-90 are such that 45 is opposite the shorter side. 45 is opposite the shorter side and 90 is opposite the hypotenuse.

Thanks Marty!

didieravoaka wrote:Now, I can clearly see that triangle 45-45-90 are such that 45 is opposite the shorter side. 45 is opposite the shorter side and 90 is opposite the hypotenuse.

Excellent. Seeing that kind of logic is just the kind of thing that you need to do in order to rock this test, Marc.