Right Triangles

Trigonometry

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

Sine

In a right triangle, the ratio of the side opposite / the hypotenuse

Cosine

In a right triangle, the ratio of the side adjacent / the hypotenuse

Tangent

In a right triangle, the ratio of the side opposite / the side adjacent

SOHCAHTOA

A mnemonic device to help remember the relationship of the three trig relationships (Sine, Cosine, or Tangent) and the sides they represent. Sine = opp / hyp ; Cos = Adj / hyp ; Tan = opp / adj

Hypotenuse

Longest side in a right triangle; opposite the right angle.

Leg of a Right Triangle

In a right triangle, the sides that include the right angle; in an isosceles triangle, the pair of congruent sides.

Right Triangle

A triangle that has a 90 degree angle.

Right Angle

90 degree angle

Pythagorean Theorem

in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs A²+B²=C²

Adjacent Side

The leg next to the given angle in a right triangle. The "adjacent side" and the hypotenuse will always create the angle of reference.

Theta

Θ - variable used in trigonometry to indicate an angle measure

Opposite Side

The side of a polygon not used to create the angle of reference. The angle of reference is composed of the hypotenuse and the side adjacent. The opposite side is the third side not touching the angle of reference.

Similar Triangles

Triangles that have the same shape but are not necessarily the same size; they have equal corresponding angles and proportional side measurements.

Complementary Angles

Two angles whose sum is 90 degrees.

4/5

4/3

15.0406

Find x using trig.

10.7

Find x using trig.

20.0

Find x using trig.

a/c

What is Sin A ?

b/c

What is Cos A?

a/b

What is Tan A?

b/c

What is Sin B?

a/c

What is Cos B?

b/a

What is Tan B?

4/5

What is sin(x)?

3/5

What is cos(x)?

4/3

What is tan(x)?

Opposite/Adjacent

What is the trig ratio for tangent of a right triangle?

Opposite/Hypotenuse

What is the trig ratio for sine of a right triangle?

Adjacent/Hypotenuse

What is the trig ratio for cosine of a right triangle?

45-45-90 triangle

x, x, x√2

30-60-90 triangle

x, x√3, 2x

rationalize the denominator

To rationalize the denominator of an expression, rewrite it so there are no radicals in any denominator and no denominators in any radical.