Question

in triangle abc, angle a is a right angle, cos(c) = 21/29, and the length of side bc is 58 units. what is the length, in units, of side ac? a 20 b 21 c 40 d 42

Explanation:

Step1: Recall the cosine formula

In a right - triangle \(ABC\) with right - angle at \(A\), \(\cos(C)=\frac{AC}{BC}\).

Step2: Substitute the given values

We know that \(\cos(C)=\frac{21}{29}\) and \(BC = 58\). Let \(AC=x\). Then \(\frac{x}{58}=\frac{21}{29}\).

Step3: Solve for \(x\)

Cross - multiply: \(29x=21\times58\). Since \(58 = 2\times29\), we have \(29x=21\times2\times29\). Divide both sides by \(29\): \(x = 21\times2=42\).

Answer:

D. 42