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

1 Answer
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.