Answer:
see explanation
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan A = =
=
, then
∠ A = (
) ≈ 41° ( to the nearest degree )
The sum of the angles in the triangle = 180° , then
∠ B + 41° + 90° = 180°
∠ B + 131° = 180° ( subtract 131° from both sides )
∠ B = 49°
Using Pythagoras' identity in the right triangle
AB² = BC² + AC² = 7² + 8² = 49 + 64 = 113 ( take square root of both sides )
AB = ≈ 10.6 ( to the nearest tenth )