Question

Which lists the side lengths in order from shortest to longest?

The figure shows a triangle whose sides are labeled as d, e, and f. The angle opposite to side d is labeled as 48 degree and the angle opposite to side f is labeled as 73 degree.

A.
d, e, f

B.
d, f, e

C.
f, d, e

D.
f, e, d

Answer 1

A. d, e, f

Explanation:

Suppose there is a triangle DEF in which,

EF = d, DF = e, DE = f, ∠D = 48°, ∠F = 73°,

∵ Sum of all interior angles of a triangle is 180°,

⇒ ∠D + ∠F + ∠E = 180°,

⇒ 48° + 73° + ∠E = 180°,

⇒ 121° + ∠E = 180°,

⇒∠E = 59°,

Now, in a triangle the angle opposite to the largest side is largest, opposite to medium angle is medium and opposite to the smallest side is smallest,

∵ ∠F > ∠E > ∠D

By the above statement,

f > e > d

Hence, FIRST OPTION is correct.