Question

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?

Answer 1

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