Awooden board is leaning against a building. the base of the board is 4 feet from the base of the building, and the base of the board forms a 65° angle with the ground. what is the length of the wooden board, to the nearest tenth?

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.

Therefore, the length of wooden board is 9.5 feet.  

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)