a traingle has an area 48 square cm and its shorter sides have lengths 9cm and 12cm. find the lagest angle of the traingle.

Answer 1

Area of triangle = side1*side2*sin(angle between them)/2

so 48 = 1/2(12)(9)sin ß
sin ß = 48/54
ß = 62.7º or 117.26º

If the angle is 62.7
Using the cosine law I found the side across from the 62.7º to be 11.226 and then using the sine law once more found the angle across from the side of 9 to be 45.44º surely making all three angles acute.

So the largest angle in the triangle must be in the second case, where the angle was 117.7º