On number 16 test 6, it says that a right trangle has 2 of its longest sides meeting at 55 degrees. How is this possible mathematically?? Wouldn't the side opposite of 55 be the second largest side since it is a larger amgle than 35 degrees?
Math destroyer question. How is this possible?
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I don't think it matters the possibility of the triangle or not just that you are able to set up the triangle in the way that they want you to based on the information they gave you. Since the two longest sides or 23 and 14. 23 obviously has to be the hypotenuse, and if you draw out a right triangle, the base has to be longer than the other side of the triangle that is not the hypotenuse. If you set up the right triangle like you would a normal 30-60-90 triangle, you see that this is the right set up in terms of triangle side lengths. The 55 degrees they give you would technically be the 30 degrees in a normal 30-60-90 right triangle.
Now if you want to solve the problem there is either two ways you can solve for the missing side which we can refer to as x. Since the 55 degrees is in the 30 degree area of a 30-60-90 degree triangle, and the hypotenuse is 23 and the adjacent triangle side is 14, to solve for x we can either make it
tan(55 degrees) = x/14 or sin (55 degrees) = x/23. Looking at the answer choices, it looks like sin (55 degrees) = x/23 is the right one to choose. if you solve for x then x becomes x = 23 (sin(55 degrees). now that you have the "height" of the triangle, you can use the triangle area formula area = bh(1/2) to get
area = 14 x (23 (sin(55 degrees) x (1/2) which reduces to 7 (23(sin(55 degrees)) which is one of the answer choices listed. Hope this helps.
Now if you want to solve the problem there is either two ways you can solve for the missing side which we can refer to as x. Since the 55 degrees is in the 30 degree area of a 30-60-90 degree triangle, and the hypotenuse is 23 and the adjacent triangle side is 14, to solve for x we can either make it
tan(55 degrees) = x/14 or sin (55 degrees) = x/23. Looking at the answer choices, it looks like sin (55 degrees) = x/23 is the right one to choose. if you solve for x then x becomes x = 23 (sin(55 degrees). now that you have the "height" of the triangle, you can use the triangle area formula area = bh(1/2) to get
area = 14 x (23 (sin(55 degrees) x (1/2) which reduces to 7 (23(sin(55 degrees)) which is one of the answer choices listed. Hope this helps.
Oh yea it does. I messed up because I knew that longest sides are opposite of largest angles and wasn't sure if meeting at 55 degrees meant something else. Should have just taken it more literally. THanks
