Question

which equation can be used to solve for c?
image of right triangle abc with right angle at c, angle at b is 35°, side bc = 5 in, side ab = c, side ac = b
options:
○ ( c = (5)cos(35^circ) )
○ ( c = \frac{5}{cos(35^circ)} )
○ ( c = (5)sin(35^circ) )
○ fourth option partially visible
mark this and return

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Solve for \( c \)

From \( \cos(35^{\circ})=\frac{5}{c} \), we can cross - multiply to get \( c\times\cos(35^{\circ}) = 5 \). Then, divide both sides by \( \cos(35^{\circ}) \) (assuming \( \cos(35^{\circ})
eq0 \)), and we obtain \( c=\frac{5}{\cos(35^{\circ})} \).

Answer:

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