Question

which equation can be used to solve for c?

options:

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

(note: the last option is partially visible as 5 but the full equation is not clear from the provided text, but the main question and the first three options are as above, along with the right triangle diagram with right angle at c, angle at b is ( 35^circ ), side adjacent to angle b (or maybe the other side) is 5 in., sides labeled c (ab), b (ac), and the 5 in. side (bc?))

Explanation:

Step1: Identify the triangle type and trigonometric ratios

This is a right - triangle with right angle at \(C\). For angle \(B = 35^{\circ}\), the adjacent side to angle \(B\) is the side of length \(5\) in, and the hypotenuse is \(c\). The cosine of an angle in a right - triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos(35^{\circ})=\frac{5}{c}\)

Step2: Solve for \(c\)

From \(\cos(35^{\circ})=\frac{5}{c}\), we can cross - multiply to get \(c\times\cos(35^{\circ}) = 5\). Then, by dividing both sides by \(\cos(35^{\circ})\), we obtain \(c=\frac{5}{\cos(35^{\circ})}\)

Answer:

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