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Question

If one angle of a triangle is 30o and the lengths of the sides adjacent to it are 40 and 403, the triangle is?

A
right angled
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B
isosceles
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C
obtuse angled
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D
none of these
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Solution

The correct options are
B isosceles
C obtuse angled
Let the unknown side be x.
Hence
cos300=402+(403)2x22(1603)
32=402+(403)2x22(16003)
4800=402+(403)2x2
(402x2)=0
x=40
Hence two sides are equal.
Hence the triangle is an isosceles triangle.

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