Special Right Triangles

Advanced GeometryTrigonometry

Lesson 2

radical – the sign that indicates a root is to be taken

radical expression – an expression containing a radical

In a 45º-45º-90º triangle, the length of thehypotenuse is times the length of a leg.2

n

Special Right Triangles

45º- 45º- 90º Triangles

n 2leg

leg

hypotenuse

A 45º-45º-90º triangle is also known as an

isosceles right triangle.

n

Examples: Find x and y.

5

5 2

x

y

The length of a diagonal of a square is 6 meters. Find the perimeter of the square.

Example:

3

3

In a 30º-60º-90º triangle, the length of the hypotenuse is twice the length of the shorter leg,

and the length of the longer leg is times the length of the shorter leg.

30º- 60º- 90º Triangles

n

n

2nlong leg

short leg

hypotenuse

Examples:

4 38

xy

Example:

The length of the altitude of an equilateral triangle is 6 feet. Find the length of a side of the triangle.

Example:

Example: Find x, y, and z.

Example: Triangle RST is a 30°-60°-90° triangle with right angle RST. is the shorter leg with endpoints S(1, 1) and T(4, 1). Locate point R in quadrant IV.

ST