Math help! Geometry triangles.?

Question

1.Draw a right traingle, ABC,
also

1.Draw a right traingle, ABC,

Answer 1

a=c*sin(30)=.5c since it is apposite the 30 degree angle
b=sqrt(c^2-a^2)= .866c
or b=c*cos(30)=.866c

a=b=c*sin(45)=.707c=

Answer 2

this question seems incorrect With the available solutions given none more desirable healthy the Pythagorean theorem. for a top attitude triangle if 7 replaced into the hypotenuse then c^2 = a^2 + b^2 ==> 40 9 = 25 + x^2 and not one of the possibles more desirable healthy at the same time as squared. If 12 replaced into the hypotenuse then one hundred forty four = 40 9 + 25 incorrect So the reply isn't to do with a top attitude triangle. to remedy for the different style an attitude 7 - 5 = 2 and the attitude will be 0 therefore it isn't 2 or a million or 12 the reply is .`. 4

Answer 3

First the first one:
Assuming C the side opposite to angle C, then side C is hypotenuse, thus by the following properties of "60°, 30°, and 90° triangles" have:
The side opposite to the 30° angle is a = (1/2)C = (1/2)6 = 3
The side opposite to the 60° angle is b = [(3^(1/2))/2]C= 3(3^(1/2))
which is a little less than.: 5.20 units.
NOTE: 3^(1/2) means square root of 3

For the second request, you should easily solve it using the Pythagorean theorem:

a^2 + a^2 = 4^2

2a^2=4^2

a^2=16/2

a = 2 square root of 2 (only take the positive value; for distances are never negative).Which is approx:2.82 units for each a and b

Not hard, hope that helped.

Answer 4

Is C the hypotenuse? If so, the other two sides are 3 and 3 sqrt 3
If C is the short leg, the other two sides are 6 sqrt 3 and 12
Is C is the long leg, the other two sides are 2 sqrt 3 and 4 sqrt 3

Again, is C the hypotenuse? Then other two sides are sqrt 2 each
If C is a leg, then the other leg is also 4 and the hypotenuse is 4 sqrt 2

Answer 5

1)
Since 90:60:30 = 2:√3:1
C=90°, B=60°, and A=30°
C=6cm then B=3√3cm (≈5.196cm) and A=3cm

2)
Since 90:45:45 = 1:1/√2:1/√2
C=90°, B=45°, and A=45°
C=4cm then B=4/√2cm (≈2.828cm) and A=4/√2cm (≈2.828cm)

Answer 6

I'm with you on this, triangles suck.
Here's the rules for 30-60-90 triangles
Given To Find
short leg long leg - multiply by square root of 3
short leg hypotenuse - multiply by 2
long leg short leg - divide by square root of 3
hypotenuse short leg - divde by 2

45-45-90 triangles
Given To Find
leg hypotenuse - multiply by square root of 2
hypotenuse a leg - divide by square root of 2

Answer 7

First off, we need to know which side is which. The values of the angles don't help to find the length of the sides if we don't know which side you've assigned each letter.

And for poor old dawgbite, -2 + -4 = -6. You add like signs.

Answer 8

45,45,90
c=square root 2 X b
b=a

30,60,90
side adjacent to 30 degree angle=square root 3 X side adjacent to 60 degree angle side,
hypotenuse= side adjacent to 60 degree angle X 2

Answer 9

Dear wandering intellect,
In the following section, I will broach on 30-60-90 triangles, 45-45-90 triangles, quadrilaterals, probability of squares, and solids(rectangular prisisms to be precise). Please sit back in your seat
and enjoy my article as I take you on an excursion to the world of
geometry.

In order for one to find a missing side in a triangle with angles that measure 30 degrees,60 degrees, and 90 degrees, one must follow the rules for a 30-60-90 triangle. One must use ratios and proportions to answer one's question. The side opposite the 90 degree angle is ?/2, the side opposite the 30 degree angle is ?/1, and the side opposite the 60 degree angle is ?/square root of 3. In order for one to answer this question, one must make a proportion. Example: If triangle ABC is a 30-60-90 triangle and angle A=90degrees, angle B=30 degrees, and angle C= 60 degrees and AC=3, what is the measure of side AB. Answer: Step: because one knows what AC equals 3, one can use a proportion to find the measure of AB. The proportion is 3/1=?/square root of 3. One has the proportion.
Step2=cross multiply. ?*1=3*square root of 3. Thus, the answer is ?=3 square root of three.
It is interesting to note that one cannot answer your question if one is not a psychic because you do not specify what sides you want one to find. Please revise your question.
In order for one to solve for a missing side in a triangle that has two angles that equal 45 degrees and one angle that equals 90 degrees, one must use ratios and proportions. One can use this datum to solve one's query: the sides opposite the 45 degree angles are in the ratio of ?/1 and the side opposite the 90 degree angle are in the ratio of ?/square root of 2.
Example: In Triangle ABC A=45, B=45, and C=90. Side AB=4. What is side BC?
Answer:Step(1) 4/square root of 2=?/1
Step(2)Cross multiply! 4*1=?*square root of 2.
Step(3)Simplify! 4=square root of 2*?
Step(4)divide square root of 2 by both sides.
The answer is ?=4/square root of 2
It is helpful to remember that if there are two equal angles in a triangle, the two sides opposite the equal angles must be equal.
Keep in mind that I omitted the angle sign in the angles. One can immediately tell that I am referring to angles when I use single capitalized letters followed by an equal sign that is followed by a measurement.
The Pythagorean Theorem can also help a squared+bsquared=c squared. This theorem only works for 90 degree triangles.
The angle opposite the longest side is the largest angle, the angle opposite the second longest side is the second largest angle, and the angle opposite the shortest side is the shortest angle. Remember that the longest side in a 90 degree triangle is called the hypotenuse and the two shorter sides in a 90 degree triangle are called the legs.
The area of a triangle is 1/2 base*height.
There might be grammatical and spelling mistakes. My spell check does not work. I was in a hurry and I did not have time to check for errors.
This succict review of triangles might help one answer queries that refer to 90 degree triangles-30-60-90 triangles and 45-45-90 triangles to be precise.
This branch of mathematics that you are studying is called geometry. Geometry comes from Geo meaning Earth and meter meaning measure. Geometry is the measure of Gaia(the third planet from the sun). To be precise, you are studying about triangles. Triangle comes from tri meaning three and angle meaning the small space between two lines that meet.
Here are some Postulates and/or theorems that might help one with similarity:ASA, SAS, and AAA.
A square can is divided into equal 90 degree triangles. If one knows the area of one triangle in the square one can multiply that by 2. By multiplying by two, one has found the area of the entire square.
It is interesting to note that a square is the word for a quadrilateral(quad=4 and lat=side) with 4 equal sides and 4 equal angles, a rhombus is a word for a quadrilateral with 4 equal sides, and a rectangle is a word for a quadrilateral with 4 equal angles.
I broached on quadrilaterals because they can be divided into 30-60-90 triangles and 45-45-90 triangles.
Another good topic I want to discuss is probability in squares.
Example question: If there is a square and half of the square is shaded and one side is equal to 3, what is the probability that one will hit the shaded region if one is trowing darts at random at the square?
Answer:Because a square has equal sides and equal angles each side equals three and each angle equals 90( i used the formula, (n-2)180[n represents the number of sides in a desired polygon]) If one draws a diagonal across, one cuts the square in half. Now the square is two 90 degree triangles. Use the formula for area, 1/2 base*height. Substitute 3 for base and 3 for height.
1/2(3)(3)=4.5, so half of the triangle is equal to 4.5.
Find the whole by multiplying 4.5 and 2. The product is 9.
The whole is 9 and the part is 4.5.
Probability equals part over whole.
Answer: The probability that you will hit the shaded region is 4.5 over 9.
Note:
I wish there was a place on this site where I could draw figures. If one wants to get a better lesson, one can ask the site to install a program that allows people to post drawings. If there is a program like this please let me know about it.
Now that I am done with my brief discursion, I will go back to the topic of geometry.
Rectangular prisisms are important because they relate to quadrilaterals. They are made up of 6 quadrilaterals. The surface area of a rectangular prism is 2(lw+lh+hw). The volume of a rectangular prism is lwh. If one has a hard time understanding the variables, one should know that l is length, w is width, and h is height. The volume is how much is inside. The surface area is the area of the surface.
With enough knowledge of geometry, one could split apart ones body into little 30-60-90 triangles and find out one's surface area.
Another related topic is coordinate geometry. Unfortunately, I will not be able to broach this topic with one. I have completed my succinct summary on geometry.
Good bye. I hope you liked my geometry banquet.
Sincerely,
Clark

Answer 10

c = a/sinA
6 = a/(sin30)
6sin30 = a
a = 6 * .5
a = 3

6 = b/sin60
b = 6sin60
b = 6(sqrt(3))/2
b = 3sqrt(3)

a = 3
b = 3sqrt(3)

------------------------------

a/sin45 = 4
a = 4sin45
a = 4sqrt(2)/2
a = 2sqrt(2)

since a and b both have the same degree, they are congruent

b = 2sqrt(2)

a = 2sqrt(2)
b = 2sqrt(2)