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06 Feb 2019, 20:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:32) correct
24%
(01:42)
wrong
based on 170
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In an isosceles triangle ABC, if ∠C = 40 degrees, and \(AB^2 + AC^2 < BC^2\), then what is the difference between the largest and the smallest angles of the triangle?
- A. 30
B. 40
C. 60
D. 70
E. 100
06 Feb 2019, 20:19
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EgmatQuantExpert
In an isosceles triangle ABC, if ∠C = 40 degrees, and \(AB^2 + AC^2 < BC^2\), then what is the difference between the largest and the smallest angles of the triangle?
- A. 30
B. 40
C. 60
D. 70
E. 100
Good question...
Few rules..
Let sides be a, b and c
(I) At \(a^2+b^2=c^2\), the triangle is right angled triangle
(II) If \(a^2+b^2>c^2\), the triangle is acute angled triangle, that is all angles are acute ( less than 90)
(III) If \(a^2+b^2<c^2\), the triangle is obtuse angled triangle, that is one angle is greater than 90.
Here we are in (III) case, so we should surely have an angle greater than 90.
Now with this info, let us check the possible angles of the triangle
(A) If 40 is the angle made twice ---- 40, 40, 100
(B) If 40 is the angle made only once ---- 40, \(\frac{180-40}{2}\), \(\frac{180-40}{2}\)-----40,70,70
In case (I) we have an angle > 90.. hence angles are 40,40,100
We are looking for the difference between the largest and the smallest angles of the triangle=100-40=60
C
General Discussion
08 Feb 2019, 00:10
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Solution
Given:
- • ABC is an isosceles triangle
• ∠C = 40 degrees
• \(AB^2 + AC^2 < BC^2\)
To find:
- • The difference between the largest and smallest angles of triangle ABC
Approach and Working:
We are given that, \(AB^2 + AC^2 < BC^2\), which implies ABC is an obtuse angles triangle at A.
- • Thus, ∠A > 90 degrees
So, for ABC to be an isosceles triangle, the only possibility is that ∠C = ∠B = 40 degrees
- • Thus, ∠A = 180 – 40 – 40 = 100 degrees
Therefore, the difference between the largest and smallest angles of triangle ABC, ∠A - ∠B = 100 – 40 = 60 degrees
Hence the correct answer is Option C.
Answer: C
