Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
Related questions
Question
Find the value of x
![4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20.
5. In AMER, ME= ER, m²M = 7x -4 and mZR = 5x + 12.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ead5a41-ff7c-4410-b111-fddf681de3b9%2Fc5781123-0668-4f87-bbfd-6c12eb95da84%2Fgd097i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20.
5. In AMER, ME= ER, m²M = 7x -4 and mZR = 5x + 12.
![7. ARAE s equinaterar
De muoIToI EquIRterau TTRangle
Corollary
An equiangular triangle is also equilateral.
Illustrative Example 2
In isosceles A CAR with base CR, mzC=2x and
mZR- x + 35, find the measures of the base angles.
R
Solution:
m2C= mZR
Based on the Isosceles Triangle Theorem
2x - x + 35
2х -х - 35
mZR= x + 35
x = 35
m2C = 2(35)
m2C - 70°
mZR - 35 + 35
mZR - 70°
Answer: The base angles are ZC and zR whose measures are 70°each.
Illustrative Example 3
Find the length of each side of AZAV given 2Z ZV.
3x - 2
x + 10
x + 4
Solution:
Because 2Z ZV, then by The Converse of the Isosceles Triangle Theorem,
AZ AV.
Based on the definition of congruent segments, AZ - AV.
AZ - AV
3x - 2 = x + 10
Зх - х - 1о+2
2x = 12
x - 6
Now replace x with 6 in the expression that represents the measure of each side.
AZ - 3x - 2
= 3(6)-2
- 18 -2
- 16
AV - x + 10
Vz - x + 4
-6+ 4
- 10
= 6+ 10
- 16
B. For Right Triangle
1. Consider two right triangles: ANHS and AFOX with right angles at H and O
respectively, such that NH = FO and HS = Ox.
N
F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ead5a41-ff7c-4410-b111-fddf681de3b9%2Fc5781123-0668-4f87-bbfd-6c12eb95da84%2F7vz20rb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. ARAE s equinaterar
De muoIToI EquIRterau TTRangle
Corollary
An equiangular triangle is also equilateral.
Illustrative Example 2
In isosceles A CAR with base CR, mzC=2x and
mZR- x + 35, find the measures of the base angles.
R
Solution:
m2C= mZR
Based on the Isosceles Triangle Theorem
2x - x + 35
2х -х - 35
mZR= x + 35
x = 35
m2C = 2(35)
m2C - 70°
mZR - 35 + 35
mZR - 70°
Answer: The base angles are ZC and zR whose measures are 70°each.
Illustrative Example 3
Find the length of each side of AZAV given 2Z ZV.
3x - 2
x + 10
x + 4
Solution:
Because 2Z ZV, then by The Converse of the Isosceles Triangle Theorem,
AZ AV.
Based on the definition of congruent segments, AZ - AV.
AZ - AV
3x - 2 = x + 10
Зх - х - 1о+2
2x = 12
x - 6
Now replace x with 6 in the expression that represents the measure of each side.
AZ - 3x - 2
= 3(6)-2
- 18 -2
- 16
AV - x + 10
Vz - x + 4
-6+ 4
- 10
= 6+ 10
- 16
B. For Right Triangle
1. Consider two right triangles: ANHS and AFOX with right angles at H and O
respectively, such that NH = FO and HS = Ox.
N
F
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