Question 245996
Determine the measurements of all angles. Since the ratio of the angles is 4:5:9 and the total of all angles in a triangle add up to 180 degrees:

{{{4x + 5x + 9x = 180}}}
{{{18 x = 180}}}
{{{x = 10}}} 

{{{4(10) = 40 degrees}}}
{{{5(10) = 50 degrees}}}
{{{9(10) = 90 degrees}}}

Draw a right triangle
Label the vertical side "10"
Label the angle opposite the vertical side "40 degrees"
(The smallest angle is always opposite the shortest side)
You will be solving for the hypotenuse (longest side); label the hypotenuse "x"

To solve for the hypotenuse use the sine function 
Sine of an angle = opposite side/ hypotenuse
{{{sin 40 = 10/x}}}
{{{x = 10/sin 40}}}
{{{x = 10/.6428}}}
{{{x = 15.55}}} degrees