Theorem Examples 30 30°-60°-90° Triangle Theorem In a 30°-60°-90° triangle, the length of the hypotenuse is 2 multiplied by the length of the shorter leg, and the longer leg is v3 multiplied by the length of the shorter leg. 10 5v3 60 30 60° 5. 22 In a 30°-60°-90° triangle, if the shorter leg length is x, then the hypotenuse length is 2x and the longer leg length is x. 60 2x 30 xV3 Use the 30°-60°-90° Triangle Theorem to find the values of x and y in AHJK. 30 Longer leg = shorter leg multiplied by V3. Divide both sides by v3. 12 = xV3 12 V3 4V3 = x 12 Rationalize the denominator. 60 y = 2x Hypotenuse = 2 multiplied by shorter leg. y = 2(4 V3) y = 8 V3 Substitute 4 V3 for x. Simplify. Find the values of x and y. Give your answers in simplest radical form. 5. 6. 30 30 60 18 60 7. 8. 60 60 30 24V3 30 33
Theorem Examples 30 30°-60°-90° Triangle Theorem In a 30°-60°-90° triangle, the length of the hypotenuse is 2 multiplied by the length of the shorter leg, and the longer leg is v3 multiplied by the length of the shorter leg. 10 5v3 60 30 60° 5. 22 In a 30°-60°-90° triangle, if the shorter leg length is x, then the hypotenuse length is 2x and the longer leg length is x. 60 2x 30 xV3 Use the 30°-60°-90° Triangle Theorem to find the values of x and y in AHJK. 30 Longer leg = shorter leg multiplied by V3. Divide both sides by v3. 12 = xV3 12 V3 4V3 = x 12 Rationalize the denominator. 60 y = 2x Hypotenuse = 2 multiplied by shorter leg. y = 2(4 V3) y = 8 V3 Substitute 4 V3 for x. Simplify. Find the values of x and y. Give your answers in simplest radical form. 5. 6. 30 30 60 18 60 7. 8. 60 60 30 24V3 30 33
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Transcribed Image Text:Name
Date
Class
Reteach
LESSON
5-8 Applying Special Right Triangles continued
Theorem
Examples
30
30°-60°-90° Triangle Theorem
In a 30°-60°-90° triangle, the length of the
hypotenuse is 2 multiplied by the length of
the shorter leg, and the longer leg is V3
multiplied by the length of the shorter leg.
10
5V3
11V3
11
30
22
60
°
60°
5
In a 30°-60°-90° triangle, if the shorter leg
length is x, then the hypotenuse length
is 2x and the longer leg length is x.
60
2x
30°
xV3
Use the 30°-60°-90° Triangle Theorem to find the values
of x and y inAHJK.
30
12 = xV3
Longer leg = shorter leg multiplied by V3.
12
= X
Divide both sides by V3.
y
12
V3
4V3 = x
Rationalize the denominator.
y = 2x
Hypotenuse = 2 multiplied by shorter leg.
60°
K
H.
y = 2(4 V3)
Substitute 4 V3 for x.
y = 8V3
Simplify.
Find the values of x and y. Give your answers in simplest radical form.
5.
6.
30
30
60°
18
60°
7.
8.
60
60°
30
24V3
30
33
Copyright O by Holt, Rinehart and Winston.
All rights reserved.
63
Holt Geometry
Transcribed Image Text:Name
Date
Class
LESSON
Reteach
5-8 Applying Special Right Triangles
Theorem
Example
45°-45°-90° Triangle Theorem
45
In a 45°-45°-90° triangle, both legs are
8V2
8
23
23
congruent and the length of the hypotenuse
is V2 times the length of a leg.
45°
45°
45
8
23V2
In a 45°-45°-90° triangle, if a leg
length is x, then the hypotenuse
length is xV2.
45°
xV2
45
Use the 45°-45°-90° Triangle Theorem to find the value of x in AEFG.
Every isosceles right triangle is a 45°-45°-90° triangle. Triangle
EFG is a 45°-45°-90° triangle with a hypotenuse of length 10.
10
F
G
10 = xV2
10
xV2
V2
V2
5V2 = x
Hypotenuse is v2 times the length of a leg.
Divide both sides by V2.
%3D
%3D
Rationalize the denominator.
Find the value of x. Give your answers in simplest radical form.
1.
2.
17
22
45°
45°
45°
3.
4.
25V2
45°
Copyright O by Holt, Rinehart and Winston.
All rights reserved.
62
Holt Geometry
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning