Final answer:
To find the length of BC given the angles and side length AC, we can use trigonometric ratios. Using the tangent ratio (tan), we can set up an equation to find BC. Solving the equation, we find that the length of BC is approximately 3.863.
Step-by-step explanation:
Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse.
Since ∠C is a right angle and ∠B is known, we can use trigonometric ratios to find the length of BC. We will use the tangent ratio (tan) since we have the opposite and adjacent sides:
tan(B) = BC/AC
tan(28.1) = BC/8
BC ≈ 8 * tan(28.1)
BC ≈ 3.863
Therefore, the length of BC is approximately 3.863.