8. Select which statement is true about the relationship between the measures of angle A(

Question

8. Select which statement is true about the relationship between the measures of angle A(<A) and angle B(<B) in the diagram shown.
A.The measure of angle A(<A) is greater than the measure of angle B(<B).
B.The measure of angle B(<B) is greater than the measure of angle A(<A). 
C.The measure of angle A(<A) is equal to the measure of angle B(<B). 
D.Cannot be determined without any other calculations.

anonymous · Answer

this is the diagram

anonymous · Answer

so I tried both 30-60-90 triangle and 45-45-90 triangle but the calculations didn't match so I think the answer is D, cannot be determined?

anonymous · Answer

like in a 30-60-90 triangle, the measure of the hypotenuse is two times that of the leg opposite the 30 degree angle and the measure of the other leg is SQRT(3) times that of the leg opposite the 30 degree angle. This didn't work out so it is not a 30-60-90 triangle

mathstudent55 · Answer

The lengths of the sides of a triangle are in the same order of size as the measures of the opposite angles.

anonymous · Answer

@mathstudent55  sorry but I don't seem to understand..:(

mathstudent55 · Answer

The bigger the length of a side, the bigger the measure of the opposite angle.

mathstudent55 · Answer

|dw:1355289292653:dw|

anonymous · Answer

oh~ ok like the hypotenuse is the opposite of 90 degrees. so, 90 degrees is the biggest angle of the triangle and the other angles should be smaller than 90 degrees

mathstudent55 · Answer

For example, in the figure I drew, since the order of length of sides is 18>17>15, then the measures of the opposite angles are in the same order. m<3 > m <2 > m<1

mathstudent55 · Answer

Yes you are right. But angles A and B are the smaller angles and you know the length of the side opposite one of them but not the length of the third side.

mathstudent55 · Answer

So you can't put the measures of angles A and B in order of size without calculating first the length of the side you don't know.

anonymous · Answer

oh ok I found the length of the third side
its sqrt 40 which is about 6.32

mathstudent55 · Answer

Notice the choices you are given. Measure of angle A bigger, smaller or equal to measure of angle B. You don't know yet. But with calculations we could figure it out. But now notice the 4th answer. It's not that there isn't enough info to figure it out. The 4th answer is that it takes more calculations to figure it out.

anonymous · Answer

oh~~~!! so its B.The measure of angle B(9>6.32 and 90degrees > angle B > angle A

mathstudent55 · Answer

You are correct in your calculation. That side is the smallest and the angle opposite that side will also be the smallest. But is that really what they are asking? Read the 4th answer carefully.

anonymous · Answer

(D.Cannot be determined without any other calculations)  is not the answer because I can determine it. the answer is B because 11>9>6.32 and 90degrees > angle B > angle A
so angle B is greater than angle A

mathstudent55 · Answer

I guess it depends on how you interpret "any other calculations" To me it means if you need to do any calculation to figure this out, it's answer 4. To you it means that if you have enough info to figure it out, you should figure it out.

anonymous · Answer

@mathstudent55  oh~ I see what you mean! hmm.. I think you are right. I'll go with number 4 and see what my teacher says, I will explain to her why I chose number 4 too! thank you:)