Upload
clinton-neal
View
213
Download
0
Tags:
Embed Size (px)
Citation preview
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 11
8-2: Special Right Triangles
G1.2.4: Prove and use the relationships among the side lengths and the angles of 30°- 60°- 90° triangles and 45°- 45°- 90° triangles.
L1.1.6: Explain the importance of the irrational numbers √2 and √3 in basic right triangle trigonometry, the importance of π because of its role in circle relationships, and the role of e in applications such as continuously compounded interest.
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 44
Isosceles Right Triangles
If a right triangle is isosceles, then it has 2 ___________ _________ and 2 ___________ __________. This means the measure of each acute angle must be ______. Thus another way to refer to Isosceles Right Triangles is as ___________ right triangles.
Isosceles Right Triangle Theorem
If each leg of an isosceles right triangle is x units long, then the hypotenuse is xtimes the square root of 2 units long.
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 66
45 - 45 - 90 Right Triangles
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 77
The triangle below is an isosceles right triangle. What is the length of the hypotenuse? Calculate your answer 2 different ways.
6
DQ 5/6/2011
An isosceles triangle has perimeter of 34.1421 feet. What is the length of the hypotenuse of the triangle?
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 1313
If one leg of an isosceles right triangle measures 15 feet, what is the perimeter of the triangle?
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 1414
What is the perimeter of the square?
8 2
Class work – 2pts 2 minutes
In an isosceles right triangle, the hypotenuse is 12. What is the length of one (1) of the sides?
A.
B.
C.
D.
E.
26
62
42
32
3
Class work – 2pts 3 minutes
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 1616
The largest triangle is equilateral
and the segment in the interior
is perpendicular to the base.
Determine the values of
x and y.
10
x
y
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 1818
30 -60 - 90 Right Triangles
When we cut an equilateral triangle with one altitude, we form 2 congruent right triangles each with one 30 and one 60 degree angle.
These are called 30 - 60 - 90 right triangles.
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 1919
30 - 60 - 90 Right Triangle Theorem
If the shortest leg of a 30-60-90 right triangle is x units long, then the hypotenuse is 2x units long and the longer leg is x times the square root of 3 units long.
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 2121
Solve for x and y
60
18
xy
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 2222
Solve for x and y
60°
y
x24
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles 2323
Solve for x and y
60°
y
34.64 x
04/19/2304/19/23 8-2: Special Right Triangles8-2: Special Right Triangles2424
An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter.