Answer:
72°
Step-by-step explanation:
The lengths 25 cm and 8 cm are the sides of the rectangle.
See the attached diagram of rectangle ABCD.
Now, let us assume the diagonal AC makes x° angle with the shorter side BC i.e.∠ BCA = x°
So, using trigonometry we can write
[tex]\tan x = \frac{AB}{BC} = \frac{25}{8} = 3.123[/tex]
⇒ [tex]x = \tan ^{-1} (3.125) = 72.25[/tex] degrees ≈ 72 degrees {Rounded to nearest degree} (Answer)
The angle formed by the short side and the diagonal of the rectangle is 72.26°°.
Rectangle are quadrilateral with four equal angles and pair of opposite sides equal to each other.
Therefore, the diagonal forms a right angle triangle. The angle formed by the short side can be found as follows:
Therefore,
tan x = 8 / 25
tan x = 0.32
x = tan⁻¹ 0.32
x = 17.7446716251
x = 17.74°
Angle formed by the shorter side = 90 - 17.74 = 72.26°
Therefore, the angle formed by the short side and the diagonal of the rectangle is 72.26°°.
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