Question

the triangle represents the roof of a new home. to estimate the cost, the framer needs to find the length of $overline{bc}$. what is the approximate length of this rafter? round to the nearest tenth. enter your answer in the box.

Explanation:

Step1: Use cosine function in right - triangle ABD

In right - triangle $ABD$, $\cos A=\frac{AD}{AB}$. We know $\angle A = 18^{\circ}$ and $AD = 13$ ft. Let $AB = BC$ (since the roof is symmetric). We first find $AB$.
$\cos18^{\circ}=\frac{13}{AB}$, so $AB=\frac{13}{\cos18^{\circ}}$.

Step2: Calculate the value of $AB$ (which is equal to $BC$)

We know that $\cos18^{\circ}\approx0.9511$. Then $AB=\frac{13}{0.9511}\approx13.7$ ft. Since $AB = BC$, the length of $BC$ is approximately $13.7$ ft.

Answer:

$13.7$ ft