The three sides of a triangle are 17, 23 and 30. Correct to the nearest tenth of a degree, what is the measure of the angle opposite to the largest side?

Question

wolf1728 · Answer

hgt² = 17² - x² 
A) hgt² = 289 - x² 

hgt² = 23² -y² 
B) hgt² = 529 -y² 

We can see from the diagram that x = 30 -y so we can input this into equation A 
hgt² = 289 - (30 -y)² 
hgt² = 289 -900 +60y -y² 

both equation A and B are both = hgt² so we can make these equal to each other 
529 -y² = 289 -900 +60y -y² 
1140 = 60y 
y = 19 and therefore 
x = 11 
arc sine (a) = 11/17 
angle a = 40.32021507 

arc sine (b) = 19/23 
angle b = 55.6988472432 

angle opposite the side of length 30 = 
40.32 plus 55.70 =
96.0 degrees