how do you get a 20 degrees angle without using a protractor or compass?

Question

my teacher set this for me and i will get 5 points/merits for my house if i find this out, so please help. I'm in desperation

Answer 1

Start with an x,y axis.

Tangent (angle) = opposite/adjacent

opposite = y coordinate, adjacent = x coordinate

Pick a number for x. Say it's 5.

Your angle is 20.

Tan (20) = y/5
y = 1.8

Plug in the points (5, 1.8)
Draw a line from (0,0) to that point

The x axis & that line make a 20 degree angle.

Answer 2

20 Degree Angle

Answer 3

You can't get a 20 degree angle. 20 degrees is 1/3 of 60 degrees. If you could construct an angle of 20 degrees, you would be able to construct a length of cos(20).

cos(60) = 4(cos 20)^3 - 3(cos 20)
4(cos 20)^3 - 3(cos 20) = 1/2
8(cos 20)^3 - 6(cos 20) - 1 = 0

You can show that 8y^3 - 6y - 1 is irreducible, so y = cos 20 is not constructible, since it is the root of an irreducible polynomial of degree 3, and constructible numbers can only be roots of irreducible polynomials of degree 2 or less. Now since cos 20 is not constructible, the angle 20 degrees cannot be constructed.

It's called trisecting the angle. Read about it at:

Answer 4

Take a sheet of A4 paper which is 210 x 297 mm

Turn it round so the long edge is nearest you and fold it in half (bring the top down to the bottom) so you now have a piece 297 x 105mm.

Draw a line from the bottom left to top right corner. You now have a 19.47 degree angle which is close enough to 20 degrees for me.

If you want to be exact, when you are folding it in half, dont bring the top all the way down but stop so the top is 4mm up from the bottom. This way you will have a piece 297 x 108mm which will give you exactly 20 degrees

Answer 5

Draw a circle and then as the point has 360 degrees divide it
by 20
360/20= 18
so you will have to cut the middle like a pie or a cake 18 times and then the angle of one of the sections is 20 degrees

Answer 6

I'm hoping you are supposed to know some trigonometry

The sin(20deg) = 0.342 = opposite side/hypotenuse
sin(70 deg) = 0.940

20 deg
|\
| \
| \ hypotenuse
| \
----\ 70 deg
opposite side (of 20 deg angle)

you need to get some graph paper


now what you need to do is determine what would be the lengths of the the triangle to get the values for the sines

well if we make the hypotenuse a value of 20 (easy multiplication)

then the side opposite the 20 deg angle would be 20*.342 = 6.84
and the side opposite the 70 deg angle would be 20 *.940 = 18.8

Now at the bottom of the graph paper, draw a horizontal line that is 6.84 cm long (can use inches but would need larger paper)

Now draw a vertical line up the left side of the graph paper starting at the left side of the 1st line draw that is 18.8 cm long. You want to make sure that the line you draw is perpendicular to the 1st line. thats why I said use graph paper then you know you have a perpendicular line.

Finally draw the hypotenuse which is a line from the end of the 18.8 cm vertical to the far right of the 6.84 cm horizontal line. The angle formed from this line and the 18.8cm vertical line will be 20 deg. (You can verify this by making sure the length of the hypotenuse it should be 20 cm long)

Good luck

Answer 7

Use trigonometry. A 20 degree angle forms a right triangle with 20,70 and 90 degrees. The three sides are referred to as the hypotoneuse, opposite and adjacent sides.

The tangent (TAN function) of an angle is the length of the opposite side divided by the length of the adjacent sides. This can be thought of as the height to length ratio.

TAN(20) = 0.364. So draw a horizontal line 1 inch long, then a vertical line 0.364 inches high. Complete the triangle, and you'll have created the right triangle described above.

Likewise TAN(70) = 2.75 or 1/(0.364)

Answer 8

I don't think you can trisect a 60 degree angle with compass and straight-edge to get your 20 degree angle. It's a classic unsolvable puzzle.

You might be able to do it with origami - however.

Let me look into this a bit.

Got it - there's a method. Have a look at this MathTrek page

Draw your 60degree equilateral triangle into the corner of your piece of paper so you have a 60degree angle (instead of the 80 degree angle they have)

Then fold your paper in half - and then fold the bottom half in half (so you get quarters).

Note point P (half way mark on left edge) and point Q (bottom left corner).

Now fold the corner so that point P goes onto your 60 degree line and point Q goes onto the quarter line and MARK THAT POINT.

Draw a line from your corner to that point and you have a 20 degree angle.

Answer 9

Get some graphing paper. Mark of a distance of 25 units. Then erect a perpendicular 9 units long.
Connect the two open ends. The smaller angle will be 19.8 degrees.

If you could construct a right triangle with legs = 250 and 91 units long, then the smaller angle would be 20.001 degrees.
I'd say that's close enough for your 5 merit points.

Answer 10

No mention that a ruler cant be used.
Ok try this.
Draw an equilateral triangle of side 3 units each.
That gives 3 angles of 60 degrees.
Mark the base of the triangle in to 3 equal sections.
Join each mark to the apex of the triangle.
You should now have 3 angles at the apex of 20 degrees each.