how to teach triangles and angles
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Answers:Well, to solve a triangle means to know all 3 angles and the length of all 3 sides. Those 2 types of triangles have interesting ratios between the sides. In the 30-60-90 triangle, imagine the shortest side (the one opposite the 30 degree angle) has a length of x. Well, the ratio of the short side to the hypotenuse is 1:2, so the hypotenuse has a length of 2x. Then the remaining side, that opposite the 60 degree angle, has a length of x times the square root of (3). So imagine that the short side has a length of 5. That means the the hypotenuse has a length of 10, and the remaining side has a length of 5 times the square root of 3. Now the 45-45-90 is easier. The two sides that aren't the hypotenuse are the same, and the hypotenuse is the length of one side times the square root of 2. So, if one side has a length of 2, then the other side also has a length of 2, and the hypotenuse has a length of 2 times the square root of 2.
Answers:equiangular - all of the angles are the same, therefore 180 degrees divided among 3 angles is 60 degrees. Think about how this would influence the lengths of the sides. scalene-all of the sides are different, which makes all of the angles different. isosceles-at least 2 (could be 3) of the sides are the same length, which makes at least 2 of the interior angles the same. equilateral- all of the sides are the same length. obtuse-one of the angles inside is bigger than 90 degrees. right- one of the angles inside is exactly 90 degrees.
Answers:You've got three angles. A = the smallest angle B= 2A - 20 C= 2A + 25 A + B + C = 180 degrees A = 180 - B - C A = 180 - (2A - 20) - (2A + 25) A = 180 - 2A +20 - 2A -25 5A = 175 A = 35 degrees B = 2(35) - 20 = 50 degrees C = 2(35) + 25 = 95 degrees 35+50+95=180
Answers:I think this is a trick question, telling you more than you need to know. It says angle C is a right angle, so sin(C) = sin(90) = 1.