Answer:
m∠B = 49°
Explanation:
Use the cosine law. b² = a² + c² - 2ac(cosB)
Since you have the lengths for three sides, you can find an angle with this law.
Lowercase letters represent the side opposite the the angle labelled with the capital letter.
AC = b = 34
AB = c = 45
BC = a = 34
Substitute the side lengths.
b² = a² + c² - 2ac(cosB)
34² = 34² + 45² - 2(34)(45)(cosB)
1156 = 1156 + 2025 - 3060(cosB) Solve some parts
1156 - 1156 - 2025 = -3060(cosB) Isolate cosB
-2025 = -3060(cosB)
cosB = -2025 ÷ -3060
B = cos⁻¹(-2025/-3060) Put this into your calculator
B ≈ 48.5654..... Round to the nearest degree.
B ≈ 49°
Angle B is about 49°.
m∠B = 49°