Question

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

Answer 1

The sides b and c meet at A, so angle A = 72°. Use the law of cosines:

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

a ≈ √105.7376 ≈ 10.3 in.

Answer: a ≈ 10.3 in.