Question

The angles of a triangle are in the ratio $3:4:5$. Find the smallest angle.

Answer 1

Given that,

The ratio of angles of a triangle$=3:4:5$

Let the angle,

$\angle A,\angle B$ and $\angle C$

then,

$\angle A:\angle B:\angle C=3:4:5$

let the ratio$=x$

then,

$\angle A=3x,\angle B=4x,\angle C=5x$

We know that,

$\angle A+\angle B+\angle C={180}^o$

$3x+4x+5x={180}^o$

$12x={180}^o$

$x={15}^o$

then,

$\angle A=3x=3\times 15={45}^o$

$\angle B=4x=4\times 15={60}^o$

$\angle C=5x=5\times 15={75}^o$

So, the smallest angle$=\angle A={45}^o$

Hence, this is the answer.