Without using a calculator solve sin 30?

Answer 1

OK.

In a right triangle, if one angle is 30 degrees, then the triangle is a 30-60-90 triangle. From geometry, the sides of a 30-60-90 triangle are in the ratio 1 : sqrt(3) : 2.

Since the sine is defined as the ratio of opposite side to hypotenuse in a right triangle, it follows that sin(30°)= 1/2 = 0.5.

Done!

BTW
The proof of the ratio of sides in a 30-60-90 triangle is obvious using a geometric proof:
Consider an equilateral triangle ABC with side length 2 and with point D as the midpoint of segment BC. Draw an altitude line from A to D. Then ABD is a 30-60-90 triangle with hypotenuse of length 2, and base BD of length 1. The fact that the remaining leg AD has length=sqrt(3) follows directly from the Pythagorean Theorem.

Answer 2

One way is to use a table. They're in the back of some math books. That's probably not what you want though. The other way only works for a few angles, like 30 degrees, 45 degrees, or 90 degrees. It's based on special triangles, like the 30-60-90 or 45-45-90. Sin is y/r, as you probably know. If you don't, it's the ratio of the y-coordinate to the hypotenuse if you draw a right triangle with the given angle at the origin and one side on the x-axis. Cos is x/r, and tan is y/x. If your angle is 90 degrees, for example, the point will end up right on the y-axis, having an x-coordinate of zero. Therefore, the cosine would be zero as well. If it's 30 degrees or 60 degrees, draw a 30-60-90 triangle. Since the sides of a 30-60-90 triangle are some multiple of 1, the square root of 3, and 2, and you only need ratios, you can just assume they are exactly those. If you want to find sin (30), just use the triangle. If you draw it, the hypotenuse will be 2 and the y-coordinate will be 1. Therefore, the answer is 1/2. 45 degree angles work the same way. If you have a larger angle, such as 150 degrees, you need to use a reference angle: the smallest angle from that to the x-axis. Draw the triangle in the new spot, remembering to include any negative x or y values.

Answer 3

First you have to construct this angle; the sum of angles in any triangle = to 180°; equilateral triangle has 3 equal angles, each being 108/3=60°; let the side be = 1, then the height will divide the foot and vertex angle by 2, thus (1/2)/1 = sin(60/2) or sin(30)=1/2;

Answer 4

you dont need a calculator for that :)
Draw a square triangle (angles of 90, 60 and 30 degrees).
Sin of the 30 degrees angle will be the oposite leg divided by hypotenuse.
1/2 or 0.5 will be the answer

Answer 5

In a rt Δ with one angle = 30 degrees, the hypotenuse is twice as long as the shortest side. By definition,
sin = (side opp)/(hypotenuse)

In a rt Δ, the side opposite 30 degrees is the shortest so
sin(30) = (opp)/(hyp) = x/2x = 0.5

Answer 6

From the Natural Sine table sine 30 = 0.5

Answer 7

Have you ever heard of the Unit Circle? It helps a lot for easy problems like this. The answer is one-half.

Answer 8

you are seriously ridiculous

in a 30-60-90 triangle the side lengths are n, 2n, and sqrt(3)n

the answer is... figure it out yourself, it is elementary

Answer 9

I wonder if you have tried it yourself as part of your learning!