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
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