How do you find the measure of the smallest in an acute triangle whose side lengths are 4m, 7m, and 8m?

1 Answer
Zor Shekhtman
Apr 20, 2015

The smallest angle lies across the smallest side, in this case it's the one that measures 4m.

Now recall the Law of Cosines:
#a^2=b^2+c^2-2bc*cos(alpha)#

In our case
#a=4m#,
#b=7m#,
#c=8m# and
#alpha# - is the smallest angle we need to measure.

Using the formula above,
#16=49+64-2*7*8*cos(alpha)#
from which
#cos(alpha)=97/112=0.86607143# (approximately)
The angle, whose cosine approximately equals to #0.86607143# is about #30^0# since #cos(30^0)=0.86602540# (approximately).

More information on the Law of Cosine you can find at Unizor by following the menu items Trigonometry - Simple Trigonometric Identities - Law of Cosine.

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