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A wooden board is leaning against a wall. The base of the board is 6 feet from the base of the wall, and the base of the board forms a 55° angle with the ground.

What is the length of the wooden board?

Enter your answer, rounded to the nearest tenth, in the box.

Respuesta :

The board is the hypotenuse of a right angle triangle. We know one side and one angle. The known side and angle are adjacent to each other so we can use the cos formula. The cos of an angle is the length of the adjacent side over the length of the hypotenuse.

CAH

Cos(55) = 6 / H
H = 6 / cos(55)
H = 10.46 or 10.5 inches (rounded)

The length of the wooden board is 10.5 feet.

The situation forms a right angle triangle.

The adjacent side of the triangle is  the length of the base of the board to the base of the wall.

The length of the wooden board is the hypotenuse of the triangle.

Therefore, using trigonometric ratio,

cos 55° = adjacent / hypotenuse

cos 55° = 6 / h

cross multiply

h = 6 / cos 55°

h = 6 / 0.57357643635

h = 10.4606807737

h ≈ 10.5 feet

learn more: https://brainly.com/question/7869956?referrer=searchResults

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