Which of the following statement is true. Explain why it is true and why the other two statement are not true?

1) If the base is twice as long as the height, then the triangle has 30 degree and 60 degree angles.





2) If the hypotenuse is twice as long as one of the legs, then the triangle has 30 degree and 60 degree angles.





3) If one side is twice as long as another side, then the triangle has 30 degree and 60 degree angles.Which of the following statement is true. Explain why it is true and why the other two statement are not true?
The statement that is true is 2. Going by the rules of a 30-60-90 triangle, the hypotenuse is 2 times a leg and the side opossite the 60 degree angle is square root of 3 times the same leg.





1 is false, because the hypotenuse is supposed to be 2 times a leg. The base and height of a triangle could be the two legs, rather than the hypotenuse.





3 is false, because if one side is twice as long as the other, this does not necessarily mean that the hypotenuse is the side that is twice as long. It is not specific enough.Which of the following statement is true. Explain why it is true and why the other two statement are not true?
1) This isn't necessarily true. You can make all kinds of different triangles where the base is twice as long as the height. For example, take a rectangle where the base is twice as long as the height, and make a triangle with the bottom two points and any point along the rectangle's top.





2) This is true. If one side's length is ';a';, the hypotenuse is ';2a';, and x is the angle across from the ';a'; side, then sin(x) = a/2a = 1/2. This means x=30, so the other angle must be 60.





3) Not necessarily true. Again, you can construct lots of different triangles like this. Take two sticks where one is twice as long as the other, and attach them at the end with a hinge. You can open and close the hinge to whatever degree you want.
2 is true by definition of a 30-60-90 triangle
sin(30) = 1/2 Sin = opposite/hypoteneuse





1. %26amp; 3. represent the same triangle, rub represent an angle whose tangent is 1/2, instead of sine.


2. is the proper situation: legs 1, sqrt(3), hypoteneuse 2.