Second angle of a triangle is two times as large as the first. Rhe third angle is 10degrees more than the second angle. What is the measurement of the first angle?
137296
ok, we can call the three sides x,y,and z respectively. all angles of a triangle have to add up to 180. so\nx+y+z=180\n\nok. y=2x and z=y+10\n\nsubstitute\nx+2x+2x+10=180 then solve for x\n\n5x+10=180\n5x=170\nx=34 degrees
448134
in a right triangle (any triangle with a 90deg angle), the hypotenuse is opposite the 90 angle.  The other two are proportional:  the smaller side is opposit the smaller angle, the (next) larger side is opposite the (next) larger angle.\n\nThe sum of the squares of both sides will equal the square of the hypotenuse.\n\nFor any integer n which is greater than 2, then a^n + b^n = c^n has no solutions in non-zero integers a, b, and c\n\nsin of an angle = opposite side/hypotenuse\ncos of an angle = adjacent side/hypotenuse\ntan of an angle = opposite side/adjacent side\n\nSOHCAHTOA\n\nthat's all you ever need to know to get through basic trigonometry.
664281
The easy way to remember this is to memorize the \n\n3 4 5 \n\nright triangle.  You will notice that any two multiples of the above will give you the other leg as a multiple.  The theorem is\n\nA^2 + B^2 = C^2,  so  3^2 + 4^2 = 5^2,  hence  9 + 16 = 25\n\nnow you have\n\n2*3 2*4 thus your other leg is 2*5\n\n6^2 + 8^2 = 10^2,  which is 36 + 64 = 100\n\nas for the angles, use the law of sines\n\nsin(90)/5 = sin(a)/3 = sin(b)/4\n\nso a = asin(sin(90)*3/5) = ~37 deg\n\nhence angles of 90 53 37
530121
x is 50 degrees. in an equilateral triangle all angles r same, so each angle is 60 because all angles in a triangle equal 180.\n\nc=x+10\n60=x+10\n-10   -10\n50=x
360180
Okay, you know that when you cut either side of a paralleogram and put it on the other side, it'll equal a rectangle and still have the same area, right?\nThe base and height will remain the same when the paralleogram is transformed into a rectangle. This rectangle can be cut perfectly into two triangles. Because the height and the base of the triangle and the rectangle are the same, then the rectangle's size will the twice the size of the triange.\nExample.\nTriangle, rectangle base: 3cm\nTriangle, rectangle height: 4cm\nArea of triangle: 3x4/2=12/2=6cm square\nArea of rectangle: 3x4=12cm square\nWe can see that the area of the rectangle is twice the area of the triangle.
626746
The angles in a triangle add up to 180, so the answer is b. 40 degrees.
654040
First of all, look at the link in my sources... It contains a picture that will help you understand what I'm trying to explain!\n\nIf the hypotenuse is 20, you know the shorter leg (x), or the leg across from the angle that measures 30°, is half of that.  You know this because of the 30°-60°-90° triangle that you will probably want to memorize for your math classes (see image).  So 20*(1/2) = 10.  x = 10.\n\nNow that you have the lengths of 2 out of 3 of the sides, you COULD simply use the pythagorean theorem to solve for y.  But if you have a calculater and your 30°-60°-90° triangle memorized, then you can do it easier and faster.  According to the image, the ratio between the shorter leg and the longer leg is 1:rt.3 (rt.3 meaning square root of 3.)  That means that all you have to do is take the length of the shorter leg, and multiply it by rt.3.  Since you know the length of the shorter leg (x) is 10, this is very easy.  10*rt.3 = 17.32.  y = 17.32\n\nIn conclusion, to answer your question, x = 10, y = 17.32.\n\nYou could also use sine and cosine formulas to solve this problem, but I personally like my way better.  If you'd like me to explain the sin and cosine way of solving this problem, hit me w/ an e-mail and I'll help if you need it!\n\nI hope I helped, and I hope my explanation wasn't too difficult to understand!  Good luck!
259401
The angles of the triangle must add to 180, and since it is isosceles, then the two base angles are the same, so the other base angle is 62 and the last angle is 180 - 2(62) = 56.  If a is the length of the base and b is the lengths of the other two sides, then.\n\na/sin56 = b/sin62\nso a = b*sin56/sin62.\n\nThen use the pythagorean theorem.  If we take a line and cut the triangle in half,  then the two halves are right triangle with hypotenuse b and one leg a.  If we let the other leg be c, then that turns out to be the height of the triangle.  So\n\nc = sqrt(b^2-a^2)\n\nThen the area is ac/2 (one-half base times height).\nnow a + 2b = 42.\nso b(2+sin56/sin62) = 42\nso b = 42/(2+sin56/sin62).\n\nThen solve for a.
307834
The first thing is to understand the difference between similar and congruent (identical).  Two triangles are similar if their shapes are similar, but their sizes may be different.  An equilateral triangle is similar to another equilateral triangle, but one could have sides of length 1 and the other sides of length 2.  These are *similar*.  But for them to be congruent both their angles and their sides would all have to be the same.\n\nLike you said, if two triangles had 2 angles the same (and therefore the 3rd angle must be known to be the same since they all add up to 180), then you've only proven them *similar*.  A side could be 3 units long, but if you doubled them all, you would still have a *similar* triangle, but it wouldn't be *congruent*.\n\nA concept commonly taught in high school mathematics is that of proving the "angle" and "side" theorems, which can be used to define two triangles as similar or congruent.\n\nIn each of these three-letter acronyms, A stands for equal angles, and S for equal sides. For example, ASA refers to an angle, side and angle that are all equal and adjacent, in that order.\n\nAAA - Angle-Angle-Angle. If two triangles share three common angles, they are *similar*. (Obviously, this means that the side lengths are locked in a common ratio, but can vary proportionally, making the triangles similar.) Additionally, since the interior angles of a triangle have a sum of 180°, having two triangles with only two common angles (sometimes known as AA) implies similarity as well. \n\nTwo triangles are *congruent* if their corresponding sides and angles are equal. Usually it is sufficient to establish the equality of three corresponding parts and use one of the following results to conclude the congruence of the two triangles:\n\nSAS (Side-Angle-Side): Two triangles are *congruent* if a pair of corresponding sides and the included angle are equal.\n\nSSS (Side-Side-Side): Two triangles are *congruent* if their corresponding sides are equal.\n\nASA (Angle-Side-Angle): Two triangles are *congruent* if a pair of corresponding angles and the included side are equal.\n\nWhile the AAS (Angle-Angle-Side) condition also guarantees *congruence*, SSA (Side-Side-Angle) does not, as there are often two dissimilar triangles with a pair of corresponding sides and a non-included angle equal. This is known as the ambiguous case. Of course, AAA (Angle-Angle-Angle) says nothing about the size of the two triangles and hence shows only *similarity* and not congruence.\n\nHowever, a special case of the SSA condition is the HL (Hypotenuse-Leg) condition. This is true because all right triangles (which this condition is used with) have a congruent angle (the right angle). If the hypotenuse and a certain leg of a triangle are congruent to the corresponding hypotenuse and leg of a different triangle, the two triangles are congruent.
209696
The answer to your question is NO!  That is assuming a rectangle that fails to pass the test as a square, i.e. two sides of one length and two sides of another length.\n\nSince you have a difference of opinions in preceding answers, may I suggest an experiment.\n\nDraw a rectangle that is 1/2 inch wide and 11 inches long.  Now draw a diagonal in that rectangle.  It should be obvious that you are NOT bisecting the angles.  \n\nIf you are trying to prove this one way or the other, look to isosolese triangles with a 90 degree vertex.  If an isosolese triangle has a 90 degree angle the base can only be opposite that angle.  By definition an isosolese triangle has equal sides and equal base angles.  That means when you apply the Pythagorean theorem the square of the sides must equal each other.  So after you have drawn the diagonal in your rectangle, that diagonal must be opposite a 90 degree corner.  That means the length of the rectangle is one side of the triangle with the width being the other.  Since the length and width of the rectangle are not equal, the sides of the triangle are not equal.  Since the sides of the triangle are not equal, the triangle is not isosolese.  Since the triangle is not isosolese, the base angles are not equal.  And since all the angles of a triangle must equal 180 degrees and one angle is known to be 90 degrees, and the other two angles are known to be unequal neither of the other two angles can equal 45 degrees.\n\nThis is a bit involved, I hope you can follow the logic.
551677
In a 45-45-90 triangle, there is an important ratio. leg-leg-hypotenuse = 1-1-square root of two.\n\nTo find the length of the leg if the hypotenuse is given...\ndivide the hypotenuse by square root of two.\nFor example... if the hypotenuse were 5, the leg would be 5/square root of 2 = about 3.5
522054
a)A=41°20’ b=17.2cm\ncos 41°20'=17.2/h\nh=17.2/cos 41 1/3°=22.9cm\n\nb) 1) A=48°40’ a=21.0cm\nsin 48 2/3°=21/h\nh=21/sin 48 2/3°=28.0cm\n\nsolve TRIANGLE ABC if \nA=50° B=81° a=95cm\n\nC=180-50-81=49°\nlaw of sines\n95/sin 50=b/sin 81=c/sin 49\nb=95 sin 81/sin 50=122.5cm\nc=95 sin 49/sin 50=93.6cm
482553
hi\nthe details which you gave have the answer for this question.\n\nangle E= angle C and angle A= angle B and DA=DB\n\nfrom this given data i will not assume that the triangles are equilateral, I will prove they are.\n\ncalculating the area of the 2 triangles with the formula (1/2)*base*height we can prove these 2 triangles are congruent and AC=BE\n\nsince the angle E=angle C and DA=DB then DB and DA must be the sides opposite these angles E and C respectively. \nhence  the line drawn(at angle of 90 degrees to base DB) from angle E to DB and line drawn(at and angle of 90 degrees to DA) from angle C to DA must be of equal magnitude (otherwise the angles cant be equal and/or sides cant be equal) ,  \n\nhence the length of this line drawn which is called as the height of the triangle is proved to be equal\n\nnow calculating the area with above formula (1/2)*base*height\nheights of 2 triangles are proved to be equal equal and bases are \ngiven to be equal hence areas of these 2 triangles must be equal.\n\nwhen area of 2 trianlges are equal and 2 sets of angles are equal and one side is equal then the 2 triangles must be absolutely congruent. hence AC must be equal to BE
21091
Theorem 6-5\nSAS Inequality TheoremIf two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. not much, but might help.
258336
The answer is C\nwell, one side's length of a triangle should be shorter than the other 2's plus (2 sides plus should be longer than one side)\nthen: 3x+4+8x+2>6x-1\n      8x+2+6x-1>3x-4\n      6x-1+3x+4>8x+2\n--> x>-7/5\n    x>3/11\n    x>-1\nThus, the answer should be x>3/11\n:)
532693
If you extend the non parallel sides to form a triangle it is right-angled as the other two angles are 33 and 57 and they sum to 90\n\nSo the requred median is a segment of a line jioning the vertex at the right angle to the midpoint of the hypotenuses of the two triangles so formed with the two parallel sides being these hypotenuses.\nNow in any right angled triangle this is the circumcentre of the triangle \nSo the distance from the lower hypotenuse to the vertex = ½ of 10 \n= 5\nAnd the distance from the upper hypotenuse to the vertex = ½ of 6\n= 3\nSo the length of the required median = 5 - 3 = 2 \n\nI think our friend above has the incorrect median.
166350
Triangles can be classified in two ways:\n\nBy the relative lengths of their sides:\n\n1.  Equilateral:  all sides are of equal length\n2.  Isosceles:  at least two sides are equal\n3.  Scalene:  all sides have different lengths \n   \nBy the size of their largest internal angle:\n\n1.  Right:  has one 90°internal angle\n2.  Obtuse:  has one internal angle larger than 90° \n3.  Acute:  all internal angles are smaller than 90°