# Right Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• One side of a right triangle is 90 °.
• The other two angles are unequal and no sides are equal.
• The hypotenuse of a right triangle is the longest side or the side opposite the right angle.
• 3 edges
• 3 vertexs
• $$a$$ = opposite leg
• $$b$$ = adjacent leg
• $$c$$ = hypotenuse

## Edge formula

$$a = \sqrt {c^2 - b^2 }$$

$$a = 2 \frac {A} {b}$$

$$b = \sqrt {c^2 - a^2 }$$

$$b = 2 \frac {A} {a}$$

$$c = \sqrt {a^2 + b^2 }$$

Where:

$$a$$ = edge

$$b$$ = edge

$$c$$ = edge

$$A$$ = area

## Perimeter formula

$$P = a + b + c$$

$$P = a + b + \sqrt {a^2 + b^2 }$$

Where:

$$P$$ = perimeter

$$a$$ = edge

$$b$$ = edge

$$c$$ = edge

## Area formula

$$A= \frac {ab} {2}$$

Where:

$$A$$ = area

$$a$$ = edge

$$b$$ = edge

## Trig Function

• Find A
• given a c: $$\; sin A= a \div c$$
• given b c: $$\; cos A= b \div c$$
• given a b: $$\; tan A= a \div b$$
• Find B
• given a c: $$\; sin B= a \div c$$
• given b c: $$\; cos B= b \div c$$
• given a b: $$\; tan B= b \div a$$
• Find a
• given A c: $$\; a= c*sin A$$
• given A b: $$\; a= b*tan A$$
• Find b
• given A c: $$\; b= c*cos A$$
• given A a: $$\; b= a \div tan A$$
• Find c
• given A a: $$\; c= a \div sin A$$
• given A b: $$\; c= b \div cos A$$
• given a b: $$\; c= sqrt (a^2+b^2)$$
• Find Area
• given a b: $$\; Area= ab \div2$$