Post on 25-Feb-2016
description
Two Special Right Triangles
45°- 45°- 90°30°- 60°- 90°
HW: Special Right Triangles WS1(side 1 only: 45-45-90)
45°- 45°- 90°
The 45-45-90 triangle is based on the square with sides of 1 unit.
11
11
11
11
45°- 45°- 90°
If we draw the diagonals we form two 45-45-90 triangles.
1
1
1
145°
45°
45°
45°
45°- 45°- 90°
Using the Pythagorean Theorem we can find the length of the diagonal.
1
1
1
145°
45°
45°
45°
45°- 45°- 90°
1
1
1
145°
45°
45°
45°
2
45°- 45°- 90°
1
1
45°
45°
In a 45° – 45° – 90° triangle the hypotenuse is the
square root of two times as long as each leg
Rule:
45°- 45°- 90° Practice
4SAME
445°
45°
45°- 45°- 90° Practice
9SAME
945°
45°
45°- 45°- 90° Practice
SAME45°
45°
45°- 45°- 90° Practice
45°- 45°- 90° Practice
45°
45°
45°- 45°- 90° Practice
= 3
45°- 45°- 90° Practice
45°
45°
3SAME
3
45°- 45°- 90° Practice
45°
45°
45°- 45°- 90° Practice
= 11
45°- 45°- 90° Practice
45°
45°
11SAME
11
45°- 45°- 90° Practice
8
45°
45°
45°- 45°- 90° Practice
8 * =
2
Rationalize the denominator
45°- 45°- 90° Practice
8
45°
45°
SAME
45°- 45°- 90° Practice
4
45°
45°
45°- 45°- 90° Practice
4 * =
2
Rationalize the denominator
45°- 45°- 90° Practice
4
45°
45°
SAME
45°- 45°- 90° Practice
7
45°
45°
45°- 45°- 90° Practice
7 *
Rationalize the denominator
45°- 45°- 90° Practice
7
45°
45°
SAME
Find the value of each variable. Write answers in simplest radical form.
• Know the basic triangles
• Set known information equal to the corresponding part of the basic triangle
• Solve for the other sides
10 2 x x 5 2 y 5 2
Find the value of each variable.Write the answers in simplest radical form.
Find the value of each variable. Write answers in simplest radical form.
Two Special Right Triangles
45°- 45°- 90°
30°- 60°- 90°
HW: Special Right Triangles WS1(side 2 only: 30-60-90)
30°- 60°- 90°The 30-60-90 triangle is based on an equilateral triangle with sides of 2 units.
2222
22
60° 60°
22
2
60° 60°
30°- 60°- 90°
The altitude cuts the triangle into two congruent triangles.
11
30°30°
30°
60°
This creates the 30-60-90 triangle with a hypotenuse a short leg and a long leg.
30°- 60°- 90°
hypotenuseShort Leg
Long
Leg
60°
30°
30°- 60°- 90° Practice
1
2
We saw that the hypotenuse is twice
the short leg.
We can use the Pythagorean
Theorem to find the long leg.
60°
30°
30°- 60°- 90° Practice
1
2
30°- 60°- 90°
60°
30°
1
2
30° – 60° – 90° TriangleIn a 30° – 60° –
90° triangle, the hypotenuse is twice as
long as the shorter leg, and the longer leg is the square root of
three times as long as the shorter leg
30°-60°-90°
60°
30°
30°- 60°- 90° Practice
4
8
Hypotenuse = short leg * 2
The key is to find the length of the
short side.
60°
30°
30°- 60°- 90° Practice
5
10
hyp = short leg * 2
60°
30°
30°- 60°- 90° Practice
7
14
* 2
60°
30°
30°- 60°- 90° Practice
3
* 2
60°
30°
30°- 60°- 90° Practice
* 2
30°- 60°- 90° Practice
60°
30°
30°- 60°- 90° Practice
11
22
Short Leg = hyp 2
60°
30°
30°- 60°- 90° Practice
2
4
60°
30°
30°- 60°- 90° Practice
9
18
60°
30°
30°- 60°- 90° Practice
23
46
60°
30°
30°- 60°- 90° Practice
14
28
60°
30°
30°- 60°- 90° Practice
9
60°
30°
30°- 60°- 90° Practice
hyp = Short Leg * 2
12
60°
30°
30°- 60°- 90° Practice
27
hyp = Short Leg * 2
60°
30°
30°- 60°- 90° Practice
20
hyp = Short Leg * 2
60°
30°
30°- 60°- 90° Practice
33
hyp = Short Leg * 2
PRACTICE
Find all the missing sides for each triangle.
Solving Strategy• Know the basic triangles• Set known information equal to the
corresponding part of the basic triangle• Solve for the other sides
Find the value of each variable. Write answers in simplest radical form.
Find the value of each variable. Write answers in simplest radical form.
30
60
12 3
2412
30
60
5.5.55
5.55.5
5.5.55
2
1010 1010
1010
2
30
60
3
21
5
1010
10
30
60
8 8 2
30
60
30
60
3 3
63
15
15
15 2
15
15
30
60
12
8 34 3
88
2 22
2
18
18
189 3
Find the distance across the canyon.
30-60-90 b
Find the length of the canyon wall (from the edge to the river).
b
cc = b * 2
Is it more or less than a mile across the canyon?
5280 ft = 1 mile