Question

the sides of a rectangle are 25 cm and 8 cm. what is the measure, to the nearest degree, of the angle formed by the short side and a diagonal of the rectangle?

Answer 1

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

$\tan x = \frac{AB}{BC} = \frac{25}{8} = 3.123$

⇒ $x = \tan ^{-1} (3.125) = 72.25$ degrees ≈ 72 degrees {Rounded to nearest degree} (Answer)