Question

In ΔABC
, find the length, to the nearest tenth of an inch, of side a if b=7
in., c=10
in., and the angle formed by these sides measures 72 degrees.(1 point)
a=

in.

Answer 1

Use the Law of Cosines (the angle between b and c is A):

a^2 = b^2 + c^2 − 2bc cos A
a^2 = 7^2 + 10^2 − 2(7)(10)cos72°
a^2 = 149 − 140(0.30901699...) ≈ 105.7376
a ≈ √105.7376 ≈ 10.2869

Rounded to the nearest tenth: a ≈ 10.3 in.