Question

If the angles of a triangle be in the ratio 1 : 2 : 7, then the ratio of its greatest side to the least side is.

• A. $1 : 2$
• B. 2 :1
• C. $( \sqrt { 5 } + 1 ) : ( \sqrt { 5 } - 1 )$
• D. $( \sqrt { 5 } - 1 ) : ( \sqrt { 5 } + 1 )$

Answer 1

Answer: (C)

$( \sqrt { 5 } + 1 ) : ( \sqrt { 5 } - 1 )$

Answer 2

$x + 2 x + 7 x = 180 ^ { \circ } \Rightarrow x = 18 ^ { \circ }$

Hence the angles are $18 ^ { \circ } , 36 ^ { \circ } , 126 ^ { \circ }$

Greatest side $\propto$ $\sin \left( 126 ^ { \circ } \right)$

Smallest side $\propto$ $\sin \left( 18 ^ { \circ } \right)$ and ratio$= \frac { \sin 126 ^ { \circ } } { \sin \left( 18 ^ { \circ } \right) } = \frac { \sqrt { 5 } + 1 } { \sqrt { 5 } - 1 }$.