• Class 11 Physics Demo

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how to teach triangles and angles

Question:I'm in geometry and just started learning about special right triangles, I'm completely lost. We're learning how to solve 30-60-90 and 45-45-90 triangles. Can anyone teach me the method to solve them? Thanks!

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.

Question:Is it possible to have an equiangular scalene triangle? is it possible to have an equiangular isosceles triangle? is it possible to have an obtuse equilateral triangle? is it possible to have a right equilateral triangle? please say YES or NO...if its a yes..please give me the degree of the 'main' angle!!! for example: if you say yes to the obtuse equilateral...can u give me the degree of the obtuse angle?! THANK YOU SOO MUCH!!! note: this is a homework assignment...i did 8 of them out of 12..i dont undertsand these four so do not think im just being lazy..i have attempted to find the answers to these questions for about an hour now and just CANNOT figure them out!!!...im taking an honors class so thats why im having a little bit of difficulty! please help me!

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.

Question:angle1 measures 20degrees less than twice the smallest angle. the third angle measures 25degrees greater than twice the smallest angle please help!? show work and/or explain. algebraic expression would be best. most of you all get my problems wrong or don't explain well enough how u got the answer so please show work. much graitude! thanx

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

Question:Angle C is the right angle and the hypotenuse is 17. The length of the side opposite angle B is 8. The length of the side opposite to A is 15. How do you find the value of sin C?

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.