Question

If an oblique triangle has side b=12
𝑏
=
12
mm long, side c=14
𝑐
=
14
mm long, ∠A=35
∠
𝐴
=
35
degrees, then what is the measure of side a to the nearest millimeter?(1 point)
a=
𝑎
=
mm

Answer 1

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

a^2 = b^2 + c^2 − 2bc cos A
= 12^2 + 14^2 − 2(12)(14) cos 35°
= 144 + 196 − 336 cos 35°
≈ 340 − 336(0.819152)
≈ 64.765

a ≈ √64.765 ≈ 8.05 mm

To the nearest millimeter: a = 8 mm.