Question

note: picture not drawn to scale
which equation can be used to find the horizontal length, r, of the illuminated area?
a. $\cos 40^{\circ}=\frac{12 \text{ ft}}{r}$
b. $\sin 40^{\circ}=\frac{r}{12 \text{ ft}}$
c. $\cos 40^{\circ}=\frac{r}{12 \text{ ft}}$
d. $\tan 40^{\circ}=\frac{r}{12 \text{ ft}}$

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the sides in the given right - triangle

Here, \(\theta = 40^{\circ}\), the adjacent side to the \(40^{\circ}\) angle is \(r\) and the hypotenuse is \(12\) ft.
So, \(\cos40^{\circ}=\frac{r}{12\mathrm{ft}}\)

Answer:

C. \(\cos40^{\circ}=\frac{r}{12\mathrm{ft}}\)