Another special right triangle is the 30°-60°-90° triangle



NOTES 5.8 : SPECIAL RIGHT TRIANGLES

Another special right triangle is the 30°-60°-90° triangle. Use an equilateral triangle to find a relationship between its side lengths.

[pic] [pic]

30°- 60°- 90° Triangle

Find the missing sides.

[pic]

| | AB | BC | AC |

|11 | 12 | | |

|12 | | 8[pic] | |

|13 | | | 4[pic] |

|14 | [pic] | | |

|15 | | 6[pic] | |

|16 | | | 12[pic] |

|17 |16[pic] | | |

|18 | | 17 | |

|19 | | | 21[pic] |

|20 | 14[pic] | | |

Special Right Triangles

A diagonal of a square divides it into 2 congruent isosceles right triangles. Since base angles of an isosceles triangle are congruent, the measure of each acute angle is 45°. Another name for this isosceles right triangle is a 45° - 45° - 90° triangle.

Use the Pythagorean Theorem to find a relationship among the side lengths of a 45-45-90 triangle

[pic]

In a 45°- 45°- 90° triangle, both legs are ______________, and the length of the _______________ is the length of the leg times _______

45° - 45° - 90° Triangle

| | AC | AB | BC |

|1 | 8 | | |

|2 | | 6[pic] | |

|3 | | | 4[pic] |

|4 | | 20 | |

|5 | 6[pic] | | |

|6 | [pic] | | |

|7 | |4[pic] | |

|8 | | | 3[pic] |

|9 | | 15 | |

|10 | 6[pic] | | |

Find the missing sides.

[pic]

| | DF | DE | EF |

|11 | 8[pic] | | |

|12 | | 4[pic] | |

|13 | | |24[pic] |

|14 | | 13 | |

|15 | 44[pic] | | |

|16 | [pic] | | |

|17 | | 6[pic] | |

|18 | | | 3[pic] |

[pic]

-----------------------

| | BC | AB | AC |

|1 | 6 | | |

|2 | | 14 | |

|3 | | | 8[pic] |

|4 | 2[pic] | | |

|5 | | 8[pic] | |

|6 | | | 10[pic] |

|7 |14[pic] | | |

|8 | | 5[pic] | |

|9 | | | 12[pic] |

|10 | 3[pic] | | |

a2 + b2 = c2

[pic]

a2 + b2 = c2

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download