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?
- PuzzlingLv 75 months agoFavourite 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°
- ted sLv 75 months ago
inverse tangent of ( 3 / 4) and π / 2 - inverse tangent of ( 3/4)
- billrussell42Lv 75 months ago
not clear what you are asking. Certainly all the angles of a rectangle are 90º