Louie is trying to find a rectangular canvas for his art project. its height must measure 18 inches and form a 48° angle with the diagonal at the top of the canvas. what is the length of the diagonal of the canvas? round your answer to the nearest inch.

The length of the diagonal of the canvas is 27 inches

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

* Lets solve the problem

- Louie is trying to find a rectangular canvas for his art project

- Its height must measure 18 inches

- The height form a 48° angle with the diagonal at the top of

 the canvas

- The height and the diagonal of the rectangle with the base of the

  rectangle formed a right triangle in which the diagonal is the

  hypotenuse and the height is the adjacent side to the angle of

  measure 48°

∵ The measure of the angle Ф = 48°

∵ The adjacent side to Ф = 18 inches

∵ The diagonal is the hypotenuse

∵ cos Ф = adjacent/hypotenuse

∴ cos 48° = 18/diagonal

- By using cross multiplication

∴ diagonal(cos 48°) = 18

- Divide both sides by (cos 48°)

∴ Diagonal = (18/cos 48°) = 26.9 ≅ 27

∵ The length of the diagonal of the canvas is 27 inches

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