Question

a triangle with right angle at c. side bc is 5 in. angle at b is 35 degrees. side ab is c, side ac is b. options: c = (5)cos(35°); c = 5 / cos(35°); c = (5)sin(35°); c = 5 / sin(35°)

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), adjacent side to \(35^{\circ}\) is \(5\) and hypotenuse is \(c\).

Step2: Rearrange the formula

From \(\cos(35^{\circ})=\frac{5}{c}\), we can solve for \(c\). Cross - multiply gives \(c\times\cos(35^{\circ}) = 5\), then \(c=\frac{5}{\cos(35^{\circ})}\).

Answer:

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