Answer:
9.5 feet.
Step-by-step explanation:
Please find the attachment.
Let L be length of wooden board.
We have been given that a wooden board is leaning against a building. The base of the board is 4 feet from the base of the building. The base of the board forms a 65° angle with the ground.
We can see from our attachment that length of the wooden board will be equal to the hypotenuse of our right triangle formed by the building and wooden board.
The distance between the base of building and base of wooden board will be adjacent side for the angle formed by the base of board and ground.
Since we know that Cosine relates the adjacent and hypotenuse of a right triangle, therefore, we will use Cosine to find the length of wooden board.
[tex]\text{Cosine}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
[tex]cos(65)=\frac{4}{L}[/tex]
[tex]0.422618261741=\frac{4}{L}[/tex]
[tex]L=\frac{4}{0.422618261741}[/tex]
[tex]L=9.4648063326032628\approx 9.5[/tex]
Therefore, the length of wooden board is 9.5 feet.
