Question

By decreasing 15 degree of each angle is a ttriangle , the ratio of their angles is 2 : 3 : 5 , the radian measure of the greatest angle .

Answer 1

ratio is 2x : 3x : 5x
therefore 2x + 3x + 5x + 15 + 15 + 15 = 180(as 15 degree has been subtracted from each angle)
10x = 145
x = 14.5
therefore 5x = 72.5
therefore 5x + 15 = 87.5 degrees
therefore largest angle is 87.5 degrees
therefore largest angle = 0.486 * (pi) = 1.527 radian

Answer 2

Answer:

1.439

Step-by-step explanation:

We are given that By decreasing 15 degree of each angle is a triangle , the ratio of their angles is 2 : 3 : 5

Let the ratio be x

So, the angles by decreasing 15 degree are 2x , 3x and 5x

Original angles are 2x+15 , 3x+15 and 5x+15

Angle sum property of triangle : The sum of all angles of triangles is 180°

So, Using angle sum property in the given triangle

$2x+15+3x+15+5x+15 = 180$

$10x+45 = 180$

$10x= 180-45$

$10x= 135$

$x=\frac{135}{10}$

$x=13.5$

So, largest angle = 5x+15 = 5(13.5)+15=82.5°

1 degree = 0.0174533 radian

67.5 degree = $0.0174533 \times 82.5$

67.5 degree = $1.439$ radian

Hence the radian measure of the greatest angle is 1.439