Answer:
m∠A = 50°
m∠B = 40°
AB = 15.5 units
Explanation:
This is a right trangle, so we can use the Pythagorean Theorem to calculate AB.
AC² + BC² = AB²
AB² = 11.9² + 10²
AB² = 141.61 + 100
AB = √241.61
AB ≈ 15.5 units
Since this is a right triangle, we only need the angle measurement of either m∠A or m∠B to calculate the angle measurement of the other.
I will use sine function to calculate the angle measurements of A and B. Try to use a more precise value for AB than the rounded answer so our angle measurement will be closer to the actual angle.
sin(m∠B) = 10/15.54381
m∠B = sin⁻¹(10/15.54381)
m∠B = 40.04°
Round to nearest tenth, so m∠B = 40°
m∠A + m∠B + 90° = 180°
m∠A + 130° = 180°
m∠A = 50°