Answer:
Answers following the rounding instructions: see below for details
BC = 5.1
m∠B = 23°
m∠V = 116°
Explanation:
Givens:
AC = 3
AB = 7
m∠A = 41°
Unknowns:
BC = ?
m∠B = ?
m∠C = ?
Find side BC using the law of cosines: c² = a² + b² - 2ab cos(C)
a² = 3² + 7² - 2(3)(7)(cos41)
a = √9 + 49 - 42(cos41)
a = 5.128 ≈ 5.13
side BC = 5.13
Use the law of sines to find m∠B: sin(A) / a = sin(B) / b = sin(C) / c
m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°
Sum of interior angles of a triangle is 180, so now you can find m∠C:
m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°
Rounding side BC to nearest tenth: BC = 5.1
Rounding angles to nearest whole degree:
m∠B = 23°
m∠V = 116°