# data[].attributes.body
for any triangle ABC with sides a, b, and c:
a^2=b^2+c^2-2bc cos A
b^2=a^2+c^2-2ac cos B
c^2=a^2 + b^2-2ab cos C

# data[].attributes.body
for any triangle ABC with sides a, b, and c: (sinA/a)=(SinB/b)=(SinC/c)

# data[].attributes.body
If two sides of one triangle are proportional to the three sides of another triangle and their included angles are congruent, then the triangles are similar

# data[].attributes.body
If the three sides of one triangle are proportional to the 3 sides of another triangle, the the triangles are similar

# data[].attributes.body
for real numbers a, b, c and d such that b and d is not equal to 0, if a/b is = to c/d, then (a+b)/b = (c+d)/b

# data[].attributes.body
In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is rad 3 times as long as the shorter leg.

# data[].attributes.body
In a 45-45-90 triangle, the hypotenuse is rad 2 times as long as a leg.

# data[].attributes.body
If the square of the longest side of a triangle is greater than the sum of the squares of the other 2 sides, then the triangle is an obtuse triang

# data[].attributes.body
If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is an acute triangle.

# data[].attributes.body
if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle

# data[].attributes.body
In the right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. C^2 = a^2 + b^2

# data[].attributes.body
If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.
Corollary 1: When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse
Corollary 2:When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg

# data[].attributes.body
a triangle with no right angle and an angle that is greater than 90 degrees

# data[].attributes.body
a vectors direction it is going to from one place to another.

# data[].attributes.body
being a vector has a certiain distance(magnitude)

# data[].attributes.body
a circle with a radius of one. in trig. the unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system.

# data[].attributes.body
a trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself

# data[].attributes.body
triangles are similar if and only if the triangles corresponding sides are in proportion and the corresponding angles are congruent.

# data[].attributes.body
a triangle with a right angle a 30 degree angle and a 60 degree angle. The smallest side is opposite the smallest angle. the medium side is the smallest side times rad 3 and biggest side is double the size of the smallest side.

# data[].attributes.body
a triangle with 2 45 degree angles and 1 90 degree angle. the adjacent sides to the 90 degree angle are equal to each other. the hypotnuse is the base side times rad 2

# data[].attributes.body
1. a law stating that the square of a side of a plane triangle is equal to the sum of the squares of the other two sides minus twice the product of the other sides multiplied by the cosine of the angle between them.

# data[].attributes.body
1.a law stating that the ratio of a side of a plane triangle to the sine of the opposite angle is the same for all 3 sides. 2.a law stating that the ratio of the sine of an arc of a spherical triangle to the sine of the opposite angle is the same for all 3 arcs.

# data[].attributes.body
inverse meaning opposite, the inverse trigonometric ratio. So it is the opposite of the functions which turns the ratio into the angle. The inverse functions are called secant, cosecant, and cotangent.

# data[].attributes.body
the longest side of a right triangle, always across from the biggest angle.

# data[].attributes.body
the opposite side is the side across from the certain side or angle.

# data[].attributes.body
from the Latin word adjacere, it means the object that is next to the object. like the side next to the angle.

# data[].attributes.body
the trigonometry function that are for right angles that is a ratio between the leg opposite to the leg adjacent.

# data[].attributes.body
the trigonometry function that are for right angles that is a ratio between the leg adjacent to the angle and the hypotnuse.

# data[].attributes.body
the trigonometry function that are for right angles is a ratio between the leg opposite the angle and hypotnuse

# data[].attributes.body
the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.