Question

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

mm

Answer 1

Use the law of cosines (A is between b and c):

a^2 = b^2 + c^2 − 2bc cos A
a = sqrt(12^2 + 14^2 − 2·12·14·cos 35°)
= sqrt(340 − 336 cos 35°) ≈ sqrt(64.77) ≈ 8.05 mm

To the nearest millimeter: a = 8 mm.