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In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...

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In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...  [#permalink]

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New post 06 Feb 2019, 18:58
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:14) correct 26% (01:45) wrong based on 19 sessions

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Re: In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...  [#permalink]

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New post 06 Feb 2019, 19:24
EgmatQuantExpert wrote:
In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units, then what is the height of the triangle?

    A. \(\frac{√3}{2}\)
    B. 1
    C. √3
    D. 2
    E. 2√3

Image



Now two cases..
(I) ∠A is the angle opposite the non-equal side, so other two sides are (180-60)/2=60.. so it is 60-60-60 an equilateral triangle
(II) ∠A is the angle opposite the equal side, so equal angles are 60 and 60 and third angle is 180-60-60=60.. so it is 60-60-60 an equilateral triangle again

Hence it is an equilateral triangle with side 2..
Height = \(\sqrt{3}\frac{side}{2}=\sqrt{3}\)

C
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Re: In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...  [#permalink]

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New post 06 Feb 2019, 19:57
given two sides are equal and one equal =60 degrees
Two situations
First situation: when one angle is 60 and other two are equal
thus 60+2x = 180
thus x = 60. therefore equilateral triangle
Second situation: when two angles equal to 60 and other being x
thus 120+x = 180
x= 60
again equilateral triangle

now height of equilateral triangle = \(\sqrt{3}/2*side\)
\sqrt{3}/2*2 = \sqrt{3}
thus C
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Re: In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...  [#permalink]

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New post 07 Feb 2019, 06:24
Iscoscales triangle with one angle as 60 will be an equilatrel triangle thus by phythogoras hieght will be root 3

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Re: In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...  [#permalink]

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New post 07 Feb 2019, 23:07

Solution


Given:
    • An isosceles triangle ABC
    • ∠A = 60 degrees
    • BC = 2 units

To find:
    • The height of triangle ABC

Approach and Working:
We know that ∠A + ∠B + ∠C = 180 degrees
    • ∠B + ∠C = 180 – 60 = 120

Now, we know in an isosceles triangles two angles must be equal
    Case 1: if ∠B = ∠C, then ∠B = ∠C = 60 degrees
    Case 2: If ∠A = ∠B or ∠A = ∠C, then all angles are equal to 60 degrees

So, we can infer that ABC is an equilateral triangle
    • Therefore, height of triangle ABC = (\(\frac{√3}{2}\)) * length of any side of ABC = (\(\frac{√3}{2}\)) * 2 = √3 units

Hence the correct answer is Option C.

Answer: C

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Re: In an isosceles triangle ABC, if ∠A = 60 degrees, and BC = 2 units ...   [#permalink] 07 Feb 2019, 23:07
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