Question

The angles of a certain triangle are in AP IF the ratio of the number of degrees in the least
angle to the number of radians in the greatest angle be as 45 : π.Express the angle in degrees​

Answer 1

${ \huge{ \pink{ \underline{ \underline{ \red{ \mathbb{ \bigstar{ \purple{answer}}}}}}}}}$

☆let the angles in degrees be a-d , a & a + d .then (a-d) +a +(a+d)=180°

=> 3a=180°

$= > a = \frac{180 \degree}{3} = 60 \degree \:$

so ,

the angle become 60° -d,60°and 60°+d

now the greatest angle in radians is

$\frac{60 \degree + d\pi}{180 \degree}$

then ,

according to the question

$(60 \degree - d) \ratio \frac{(60 \degree + d)\pi}{180 \degree} = 45 \degree \ratio \: \pi \\ = > \frac{(60 \degree - d)180 \degree}{(60 \degree + d)\pi} = \frac{45 \degree}{\pi} \\ = > \frac{60 \degree - d}{60 \degree + d} = > \frac{45 \degree}{180 \degree} = \frac{1}{4}$

=> 4(60°-d)=60° +d =240°-4d=60°+d

=> 4d+d=240°-60°=> 5d=180°

=> d=180°/5

=> d=36°

✧so angles become 60°-36°=24°;60°;60°+36°=96°

❁Hence ,

the angles in degrees are 24°,60° and 96°

_______________________________

Answer 2

=> d=36°

________________________________

so angles become 60°-36°=24°;60°;60°+36°=96°

________________________________