Question 245996: The shortest side of a triangle is 10. The angle ratios are 4:5:9. What is the length of the longest side? Answer by marcsam823(57) (Show Source):
You can put this solution on YOUR website! 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:
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 degrees
(