which if the following sets of measurement are side length of an obtuse triangle?
a) 3,4,5
b) 2,3,3
c) 4,5,7
d) 6,7,8
Answers
Given : side length of a triangle
To Find : which if the following sets of measurement are side length of an obtuse triangle
a) 3,4,5
b) 2,3,3
c) 4,5,7
d) 6,7,8
Solution:
In obtuse triangle angle opposite to largest side will be more than 90°
Using cosine rule
c² = a² + b² - 2ab CosC
CosC must be negative for angle to greater than 90°
CosC = (a² + b² - c²)/2ab
=> a² + b² - c² < 0
a) 3,4,5
3² + 4² - 5² = 0
Not obtuse angled ( but right angle triangle )
b) 2,3,3
there is no unique largest side
can not be obtuse angled
c) 4,5,7
4² + 5² - 7²
= 16 + 25 - 49
= - 8 < 0
Hence obtuse angle triangle
d) 6,7,8
6² + 7² - 8²
= 36 + 49 - 64
= 85 - 64
= 21 > 0
not an obtuse angled triangle
4,5,7 are side length of an obtuse triangle
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Given :- which if the following sets of measurement are side length of an obtuse triangle?
a) 3,4,5
b) 2,3,3
c) 4,5,7
d) 6,7,8
Answer :-
checking all option we get,
a) 3, 4, 5
as we can see that,
→ 3² + 4² = 5²
→ 9 + 16 = 25
→ 25 = 25
satisfy right angled ∆ property , so its a right angle .
b) 2, 3 ,3
as we can see that, we have two sides are of equal. we know that large side has greater angles , but a triangle cant have 2 obtuse angles . so this option is also not correct .
c) 4, 5 , 7
using cosine rule,
→ 7² = 4² + 5² - 2*4*5*cosA
→ 49 = 16 + 25 - 40*cosA
→ 49 - 41 = (-40)cosA
→ 8 = (-40)cosA
→ cosA = (8/-40) = (-1/5)
→ cos A = (-0.2)
→ A = cos^(-1)(-0.2)
→ A ≈ 101.5°
therefore, Option (C) is correct answer.