Question

The picture below shows a barn door: What is the length of the bar AC? 6 sin 60° 6 cos 60° 6/cos 60° 6/tan 60°

Answer 1

Okay, here we have this:

Considering the provided graph and measures, we are going to calculate the requested length, so we obtain the following:

We can clearly see from the graph that there is an angle of 90 degrees, so we can use the trigonometric ratios to find the missing sides. In this case we know an angle, the hypotenuse and we want to know the adjacent leg, and the ratio that relates these measurements is the cosine, so we have:

cos(tetha)=adj/hyp

$cos(60)=\frac{AC}{6\text{ ft}}$

Let's solve for AC:

$AC=6cos(60)\text{ ft}$

Finally we obtain that the correct answer is the second option. The length of the bar AC is equal to 6cos 60° ft.