F asked in Science & MathematicsMathematics · 5 months ago

A rectangle piece of plywood 3 ft x 4 ft is cut from one corner to the opposite corner. What are the angles between the edges of the pieces?

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  • 5 months ago
    Favourite answer

    First, use the Pythagorean Theorem (or your memorization of common Pythagorean Triples) to figure out the length of the diagonal.

    3² + 4² = c²

    9 + 16 = c²

    25 = c²

    c = √25

    c = 5

    So the diagonal is 5 feet.

    Now draw your right triangle with sides of 3-4-5. 

    Let α be the angle opposite side 3.

    Let β be the angle opposite side 4.

    Using your trigonometric ratios:

    sin(angle) = opposite / hypotenuse

    sin(α) = 3/5

    α = arcsin(3/5)

    α ≈ 36.87°

    sin(β) = 4/5

    β = arcsin(4/5)

    β ≈ 53.13°

    Attachment image
  • ted s
    Lv 7
    5 months ago

    inverse tangent of ( 3 / 4) and π / 2 - inverse tangent of ( 3/4)

  • 5 months ago

    not clear what you are asking. Certainly all the angles of a rectangle are 90º

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