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Answer :
Answer:
90⁰
Step-by-step explanation:
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Final answer:
The diagonal of the rectangles forms two angles with the sides, about 32 degrees and 58 degrees respectively. These are found using the Pythagorean theorem to find the length of the diagonal, and then the arctan function to find the angles.
Explanation:
To find the angle that the diagonal makes with the sides of the rectangle, first calculate the length of the diagonal which can be found using the Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this as: c² = a² + b². In this case, the length and width of the rectangle are the two sides (a and b) and the diagonal is the hypotenuse (c).
So a = 68 inches, b = 42 inches. Plugging these into our formula gives: c² = 68² + 42², so c = √[(68²) + (42²)] which approximates to 80 inches.
Next, calculate the angles using the inverse tangent (or arctan) function: θ = arctan(opposite/adjacent). In this case, the angles are = arctan(42/68) and arctan(68/42). This gives us angles of approximately 32 degrees and 58 degrees.
Learn more about Angles of a Rectangle
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