Homework Help is Here – Start Your Trial Now!
Math
Geometry
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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
See similar textbooks
Question
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 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
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
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
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS