final answer
B. 4.2. This is determined by applying the trigonometric relationship of a right-angled triangle, specifically the cosine function, where the cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse.
Explanation.
The length of AB to the nearest tenth is found to be 4.2 units. This is determined by applying the trigonometric relationship of a right-angled triangle, specifically the cosine function, where the cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse. Given that angle C is 42 degrees and side AC is 5 units, using the cosine function (cos = adjacent/hypotenuse), AB can be calculated by multiplying the adjacent side (AC) by the cosine of angle C. Therefore, AB = AC × cos(C) = 5 × cos(42°) ≈ 4.2 units.
In this scenario, the cosine function helps in solving for the unknown side length by utilizing the given angle and adjacent side of the right triangle. By substituting the known values into the cosine function formula, the missing side length (AB) can be accurately approximated. Thus, rounding to the nearest tenth, AB is approximately 4.2 units, providing the solution for the length of side AB in the given triangle. This method allows for the determination of unknown side lengths in right triangles when an angle and one side length are known.