Let a, b and c be the sides of the triangle.
Where a and b are the lengths of the two shorter sides and c be the length of the longest side.
Classify the triangle as acute, right, or obtuse, explain.
Problem 1 :
Solution:
Let c represent the length of the longest side of the triangle.
c^{2} ? a^{2} + b^{2}
6^{2} ? 5^{2} + 2^{2}
36 ? 25 + 4
36 > 29
Because c^{2} is greater than a^{2} + b^{2}, the triangle is obtuse.
Problem 2 :
Solution:
Let c represent the length of the longest side of the triangle.
c^{2 }? a^{2} + b^{2}
17^{2} ? 8^{2} + 15^{2}
289 ? 64 + 225
289 = 289
Because c^{2} is equal to a^{2} + b^{2}, the triangle is right.
Problem 3 :
Solution:
Let c represent the length of the longest side of the triangle.
c^{2 }? a^{2} + b^{2}
72 ? 7^{2} + 7^{2}
49 ? 49 + 49
49 < 98
Because c^{2} is less than a^{2} + b^{2}, the triangle is acute.
Use the side lengths to classify the triangle as acute, right, or obtuse.
Problem 4 :
7, 24, 24
Solution:
By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.
Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.
c^{2} ? a^{2} + b^{2}
24^{2} ? 7^{2} + 24^{2}
576 ? 49 + 576
576 < 625
Because c^{2} is less than a^{2} + b^{2}, the triangle is acute.
Problem 6 :
7, 24, 25
Solution:
By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.
Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.
c^{2} ? a^{2} + b^{2}
25^{2} ? 7^{2} + 24^{2}
625 ? 49 + 576
625 = 625
Because c^{2} is equal to a^{2} + b^{2}, the triangle is right.
Problem 7 :
7, 24, 26
Solution:
By Triangle Inequality Theorem, the above set of numbers can represent the side lengths of a triangle.
Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides.
c^{2} ? a^{2} + b^{2}
26^{2} ? 7^{2} + 24^{2}
676 ? 49 + 576
676 > 625
Because c^{2} is greater than a^{2} + b^{2}, the triangle is obtuse.
Determine whether the triangle is acute, right, or obtuse.
Problem 8 :
Solution:
Let c represent the length of the longest side of the triangle.
c^{2} ? a^{2} + b^{2}
5^{2} ? 4^{2} + 4^{2}
25 ? 16 + 16
25 < 32
Because c^{2} is less than a^{2} + b^{2}, the triangle is acute.
Problem 9 :
Solution:
Let c represent the length of the longest side of the triangle.
c^{2} ? a^{2} + b^{2}
14^{2} ? 12^{2} + 6^{2}
196 ? 144 + 36
196 > 180
Because c^{2} is greater than a^{2} + b^{2}, the triangle is obtuse.
Problem 10 :
Solution :
Let c represent the length of the longest side of the triangle.
c^{2} ? a^{2} + b^{2}
15^{2} ? 12^{2} + 9^{2}
225 ? 144 + 81
225 = 225
Because c^{2} is equal to a^{2} + b^{2}, the triangle is right.
Problem 11 :
Match the side lengths of a triangle with the best description.
1) 2, 10, 11 2) 8, 5, 7 3) 5, 5, 5 4) 6, 8, 10 |
A. right B. acute C. obtuse D. equiangular |
Solution:
1) By Pythagorean Theorem,
11^{2} = 2^{2} + 10^{2 }
121 = 4 + 100
121 > 104
It is obtuse triangle.
2) By Pythagorean Theorem,
7^{2} = 8^{2} + 5^{2}
49 = 64 + 25
49 < 89
It is acute triangle.
3)
5, 5, 5
It is equiangular triangle.
4) By Pythagorean Theorem,
10^{2} = 6^{2} + 8^{2}
100 = 36 + 64
100 = 100
It is right triangle.
1) 2, 10, 11 2) 8, 5, 7 3) 5, 5, 5 4) 6, 8, 10 |
C. obtuse B. acute D. equiangular A. right |
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM