Question

What is the length of the wood that is needed to replace AD?

Answer 1

4.2 inches

Step-by-step explanation:

First, we need to calculate the length of AB. It can be calculated using the trigonometric function tangent because

`\begin{gathered} \tan(45)=\frac{\text{ Opposite side}}{Adjacent\text{ side}} \\ \\ \tan(45)=(AB)/(10) \end{gathered}`

Because 45 = 30 + 15. Now, we can solve for AB as follows

`\begin{gathered} 10\cdot\tan(45)=AB \\ 10\cdot1=AB \\ 10=AB \end{gathered}`

Using the same trigonometric function, we can calculate the length of DB, so

`\begin{gathered} \tan(30)=\frac{\text{ Opposite side}}{\text{ Adjacent side}} \\ \\ \tan(30)=(BD)/(10) \\ \\ 10\cdot\tan(30)=BD \\ 10\cdot0.5774=BD \\ 5.77=BD \end{gathered}`

Now, the length of AD is equal to

AD = AB - BD

AD = 10 - 5.77

AD = 4.23

Therefore, the answer is 4.2 inches