Chapter 8.4, Problem 12CE

To determine

To calculate:Are the lengths of the sides in the same ratio.

Answer to Problem 12CE

No.

Explanation of Solution

Given information:

Measures of the angles of a tringle are in the ratio $1:2:3$ .

Calculation:

For a tringle, the sine rule is given by,

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ ,

where $a,b,c$ are the lengths of the sides of a triangle, and $A,B,C$ are the angles of the triangle opposite to the sides $a,b,c$ , respectively.

Now, since the measures of the angles of a tringle are in the ratio $1:2:3$ , by the sine rule the lengths will be in the ratio of sines of an angle, which will be, $\sin x:sin2x:sin3x$ , which is not cannot be same as $1:2:3$ .