I need a 30-60-90 Triangle Proof that doesn't involve sin, cos, or tan.?

Question

I need a 30-60-90 Triangle Proof that doesn't involve sin, cos, or tan.

Answer 1

If this is not what you want, i've inclued the page with a bunch of them. And if you can't find it there try the google page.
The proof

Here is the proof that in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : . It is based on the fact that a 30°-60°-90° triangle is half of an equilateral triangle.

Draw the equilateral triangle ABC. Then each of its equal angles is 60°. (Theorems 3 and 9)
A 30-60-90 triangle

Draw the straight line AD bisecting the angle at A into two 30° angles.
Then AD is the perpendicular bisector of BC (Theorem 2). Triangle ABD therefore is a 30°-60°-90° triangle.

Now, since BD is equal to DC, then BD is half of BC.

This implies that BD is also half of AB, because AB is equal to BC. That is,

BD : AB = 1 : 2

From the Pythagorean theorem, we can find the third side AD:
AD² + 1² = 2²
AD² = 4 − 1 = 3
AD = .

Therefore in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : ; which is what we set out to prove.

Answer 2

30-60-90 Triangle Theorem

Answer 3

You mean, a proof of the ratio of the sides? Start with an equilateral triangle of side 2x. Drop an altitude from one of the angles - it will bisect the opposite side. You now have a 30-60-90 triangle with hypotenuse 2x and one leg x. The Pythagorean Theorem will give you the other leg.

Answer 4

to discover the trig applications of 30-60-ninety ranges, you could determine it out truthfully quite than memorizing and forgetting. Draw an equilateral triangle, and label the two aspects 2. cut back it in a million/2, bisecting a 60-degree attitude and forming a genuine attitude on the backside. you're actually drawing the altitude of the equilateral triangle. Now you have 2 30-60-ninety real triangles, so in simple terms paintings with one. The hypotenuse, which replaced into an component of the equilateral, is two, and the component that replaced into halved is a million. super, now you have have been given 2 aspects of a genuine triangle and might truthfully use the Pythag. Thm. to discover the 0.33 (that's the altitude of the equilateral triangle). you in addition to could understand that the attitude that replaced into halved is your 30. Now you have have been given all 3 angles, all 3 aspects, and might use SOH, CAH, TOA to your 30 and 60. For the ninety, you will ought to bypass to the unit circle. ninety ranges is on the precise of the y-axis on the unit circle. The coordinates there are (0,a million) super! y is sine ("why sign") and x is cosine, so, back that's uncomplicated to work out. that's it! i'm hoping this helped! in case you already comprehend it, you will never have a difficulty with those applications. :)

Answer 5

ok its easy that what i am doing in my formal geomerty class.

U have to say that the hypotheue is 2x and
adjecent to 30 degree is xroot3
and the side adjecent to 60 is x and if x = and thing. The angles will always === 30-60-90.
U can prove 2 sides then the other has to be 90. Its a theorm.

Answer 6

a²+b²=c²
c being the side across from the 90 degree angle.

Answer 7

The short side is equal to one half the hypotenuse.

Answer 8

use the pythagorean theorem

Answer 9

sorry that is impossible go find it in ur geometry text u lazy bum