Question

ac =
round your answer to the nearest hundredth.
7 of 10

Explanation:

Step1: Identify trigonometric relation

In right - triangle \(ABC\) with right - angle at \(C\), we know the hypotenuse \(AB = 7\) and angle \(B=40^{\circ}\), and we want to find the adjacent side \(AC\) to angle \(B\). We use the cosine function: \(\cos B=\frac{AC}{AB}\).

Step2: Rearrange the formula

We can rewrite the formula as \(AC = AB\times\cos B\).

Step3: Substitute values

Substitute \(AB = 7\) and \(B = 40^{\circ}\) into the formula. So \(AC=7\times\cos(40^{\circ})\).

Step4: Calculate the value

Using a calculator, \(\cos(40^{\circ})\approx0.766\), then \(AC = 7\times0.766 = 5.362\).

Step5: Round the answer

Rounding \(5.362\) to the nearest hundredth gives \(5.36\).

Answer:

\(5.36\)