Question

a
b
c
c
5 in.
35°
b
c=(5)cos(35°)
c = \frac{5}{cos(35°)}
c=(5)sin(35°)
c = \frac{5}{sin(35°)}
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Explanation:

Step1: Recall cosine definition in right - triangle

In right - triangle \(ABC\) with right - angle at \(C\), \(\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(B = 35^{\circ}\), the side adjacent to angle \(B\) is \(b = 5\) inches and the hypotenuse is \(c\).
So, \(\cos(35^{\circ})=\frac{5}{c}\).

Step2: Solve for \(c\)

Cross - multiply the equation \(\cos(35^{\circ})=\frac{5}{c}\) to get \(c\times\cos(35^{\circ}) = 5\), then \(c=\frac{5}{\cos(35^{\circ})}\).

Answer:

\(c=\frac{5}{\cos(35^{\circ})}\)