A triangular plot of land has sides of lengths 410 feet, 360 feet, and 170 feet. Approximate the smallest angle (in degrees) between the sides. (Round your answer to the nearest whole number.)

Answer 1

the smallest angle will be the one opposite the shortest side
if a = 410 and b = 360 and c = 170 we want angle C
but we all know the law of cosines
c^2 = a^2 + b^2 - 2 a b cos C
170^2 = 410^2 + 360^2 - 2*410*360 cos C
solve for cosC
then find cos^-1 C

Answer 2

the law of cosines gives this quickly:
ie: the angle between the 410 and 360 sides is
170^2=410^1+360^2 - 2*410*360*cos Angle1
solve for angle1
then get a second angle angle 2
360^2=410^1+170^2-2*410*170*cos2
solve for cosine 2
then knowing all three angles add to 180, solve for angle 3
After you have done that, make a sketch with just three sides. You wlll come to the conclusion that the smallest angle will always be between the two longest legs (angle1 here).