For the 30-60-90 triangle I always have trouble finding the answer?

Question

For the 30-60-90 triangle I always have trouble finding the answer?
When all they give is the number where the square root 3 is.
I also have trouble getting that number.
I only know how to use an caculator on these stuff. So i get decimals. And I always get points off for that.
Help?
Thanks

Answer 1

My Pre-calc teacher showed me this neat little trick i always use:

If you set up a chart of the main angles: 0, 30, 45, 60, 90
The sin values follow

sqrt(0)/2, sqrt(1)/2, sqrt(2)/2, sqrt(3)/2, sqrt(4/2)
Which can be simplified to

0, 1/2, sqrt(2)/, sqrt(3)/2, 1

The cos values are reversed, so they are

1, sqrt(3)/2, sqrt(2)/2, 1/2, 0

Tangent can be found by dividing the sin values by the cosine values.

Answer 2

A 30-60-90 triangle is nothing but half an equilateral triangle (triangle with all sides equal and all angles equal to 60 degrees).
Assume that the side of the equilateral triangle is 'a'. Assuming that 30 degree is the top angle - the hypotenuse (side opposite the 90 degree) is length 'a' and the base is a/2. Let the perpendicular be 'h'.
Apply Pythagoras' Theorem
a^2 = (a/2)^2 + h^2
h^2 = a^2 - (a^2)/4 = (3a^2)/4
h = (a/2)sqrt(3)
for 60 degree
sin 60 = perpendicular / hypotenuse
= ((a/2)sqrt(3)) / a = (a sqrt(3))/2a = sqrt(3)/2
cos 60 =base / hypotenuse
= (a/2) / a = a / 2a =1/2
tan 60 = perpendicular / base
= ((a/2)sqrt(3)) / (a/2) = (2a sqrt(3))/2a = sqrt(3)

for 30 degree - take this triangle and turn it so that the perpendicular becomes the base. Now the previous base will be the perpendicular.
Thus
base = (a/2)sqrt(3)
perpendicular = a/2
sin 30 = perpendicular / hypotenuse
= (a/2) / a = a / 2a =1/2
cos 30 =base / hypotenuse
= ((a/2)sqrt(3)) / a = (a sqrt(3))/2a = sqrt(3)/2
tan 30 = perpendicular / base
=(a/2) / ((a/2)sqrt(3)) = 2a / (2a sqrt(3))= 1 / sqrt(3)

Hope this helps.

Answer 3

Gosh honey I really feel bad for you. First if they want you to calculate the square root of a number there are two ways to do it without a calculator. One way is a form of trial and error where you take a number and try it than subtract it from the root and on and on. Any Algebra book will have the exact method. The second way is really out of the Dark Ages and involves Logarithms. Without going into the math you look up the log of 3 (base 10) than divide that number by 2 for the square root than look up the anti log of the resulting quotient.

Now if you're into Greek culture why not try the Pythogrean Theorem on the right triangle. C(squared) = A(squared)+ B(squared). C is the hypothenuse, A and B are the legs of any right (90 degree) triangle.

Don't cry honey. If a girl like me can learn math so can a guy like you. After all men are better in math than girls lol lol.

Answer 4

Area=1/2 b*h

Answer 5

Quite simple & easy.

Imagine the Triagle ABC in which measure of Angle b (Opposite to the side AC) = 90 Degrees, the measure of Angle a (opposite to the side BC = 60 degrees & the measure of angle c (opposite to the side AB) = 30 degrees.

The ratio of the angles c : a : b = 30 degrees : 60 Degrees : 90 Degrees or 1: 2: 3

The Ratio of the sidesAB (opposite to angle c) : Side BC (ooposite to angle a) : side AC (opposite to angle b) = 1 : root 3 : 2

We know the values of 1 & 2 the whole numbers.

Square root of 3 = 1.732.(correct to 3 decimal places)

Using this you can do any sum.

Suppose the hypotenuse AC = 2 parts=10 feet. Find the other sides.

SideAB = 1 part = 5 feet

Side BC = Root 3 parts = 1.732 times 5

= 8.660 or 8.66.

Answer 6

The side opp to 30 is always = x
The hypotenuse = 2*x
The side opp to 60 is always = square root 3 * x

So if any of the sides are given, you can find the values of the other 2 sides by the above formulae.

Answer 7

Since 60 is greater than 30, the side opposite 60 is sqrt(3), which is greater than 1, the side opposite 30.

Answer 8

Draw a right angled triangle right angled at C
AC is vertical = √3
AB is hypotenuse = 2
BC is horizontal = 1

From this triangle and using SOH,CAH,TOA:-

------sin------cos-----tan
A----1/2----√3/2----1/√3
B---√3/2----1/2-----√3/1

Answer 9

do it as a fraction