17) length of angle problem

Question

The length of the sides of angle ABC are consecutive integers. If angle ABC has the same perimeter as an equilateral triangle with a side angle of 9, what's the len of the shortest wide angle abc?? 

Answer 1

27 = x-1 + x + x+1 = 3x

x =27/3= 9

x-1 = 8 for the shortest side

8, 9 and 10 are the 3 sides

but you do have "side angle" which must be a typo

equilateral triangles all have 3 60 degree angles,never 9 degrees

with 3 equal sides of 9 each in this problem

You could use laws of sines and cosines to calculate the angles opposite sides 8, 9 and 10

sinA/8 =sinB/9 = sinC/10

or 8^2 = 9^2 + 10^2 - 2(9)(10) cosA

64 = 181 - 180cosA

cosA = 117/180

A = cos^-1A(117/180) = the angle whose cosine = 0.65, which is about 49.46 degrees

81 = 64 + 100 - 2(80)cosB

cosB = 83/160

B = 58.75 degrees

100 = 81+64 -2(8)9cosC

cosC = 45/144

C = 71.79 degrees

angle opposite the shortest side is about 49.5 degrees