right triangles?

Question

trigonometri

Answer 1

Okay, here is stuff about right triangles and trigonometry.

1. A right triangle always has three sides and three angles, one of which is 90 degrees (a right angle).

2. The side across from the right angle is called the hypoteneuse. The other two sides are called legs.

3. The square on the hypoteneuse equals sum of the squares on the legs. This is the Pythagorean Theorem.

4. Except for the right angle, each angle has one leg opposite and one leg, not the hypoteneuse, adjacent.

5. For an angle x, three trig functions are defined as:

sine x = opposite/hypoteneuse
cosine x = adjacent/hypoteneuse
tangent x = opposite/adjacent

These are abbreviated as sin x, cos x, tan x.

6. There are three more trig functions -- cosecant, secant, and cotangent -- defined as the reciprocals of sine, cosine, and tangent. They are abbreviated as csc x, sec x, and cot x or ctn x.

7. Given the value of a trig function, you can get the value of the angle. This is the "inverse" process, sometimes referred to as "arc". So if y = sin x, then x = arcsin y or sin^(-1) y.

8. Often in trigonometry, people prefer "radian measure" over degree measure. The relation "pi radians equals 180 degrees" allows two-way conversion.

Everything in trigonometry follows from what I've written above.

Answer 2

A right triangle is a triangle with a right (90 degrees) angle.

The side across from the right angle is called hypotenuse, the other sides, legs.

The hypotenuse is the longest side. The Pythagorean Theorem states that
(hypotenuse)^2 = (leg 1)^2 + (leg 2)^2

Some right triangles have all rational lengths. These form "Pythagorean triples". Examples are (3, 4, 5); (5, 12, 13); (8, 15, 17).

Because the sum of angles in a triangle are 180 degrees, the two non-right angles must have sum 90 degrees, that is, they are complements. The smallest angle is found opposite the smallest side.

If the right triangle is isosceles (legs have same length), the angles are 45-45-90 degrees, and hypotenuse = sqrt 2 as long as each of the legs.

As in every triangle, the ratio between any two sides is only depending on the angles. In a right triangle, only one of the (non-right) angles needs to be known to know all angles; therefore, if one angle t <> 90 degrees is known, six ratios are determined. Calling the leg across the known angle t, "opposite" leg, and the other leg "adjacent", we find the trigoniometric ratios

opp. / adj.: tangent of t (tan, tg)
opp. / hyp.: sine of t (sin)
adj. / hyp.: cosine of t (cos)
adj. / opp.: cotangent of t (cot, cotg)
hyp. / opp.: cosecant of t (csc)
hyp. / adj.: secant of t (sec)

If a vertex is drawn from the vertex with the right angle onto the hypotenuse, it divided the right triangle into two smaller right triangles, similar to the original triangle and to each other. The length of the altitude is

(altitude) = (leg 1) * (leg 2) / (hypotenuse)

The other two altitudes in a right triangle are trivial; they coincide with the two legs.

The area of a right triangle is
(area) = (leg 1) * (leg 2) / 2
(area) = (hypotenuse) * (altitude) / 2

Answer 3

a right triangle is a triangle with one 90 degree angle and the other 2 angles must add up to 90. right triangles are used in trig to find their angles. sine, cosine, and tangent.

Answer 4

There are lots of things one can know about right triangles -- far too many to list here without some clue as to what specifically is needed.

Answer 5

a triangle in which one of the angles is 90 degree n which satisfies pythagoras theorem i.e (hypotenuse)^2=(base)^2+(altitude)^2