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?

A. 18°
B. 72°
C. 90°
D. 112°

Answer 1

Using trigonometry and the tangent function, one can calculate the angle formed by the short side and a diagonal of a rectangle as approximately 72°, which is option B.

Step-by-step explanation:

To find the measure of the angle formed by the short side and a diagonal of the rectangle, we need to use trigonometry. In a rectangle, a diagonal forms two congruent right triangles with the sides of the rectangle. Let's focus on one of those right triangles. We have one side that is 8 cm (the short side) and another side that is 25 cm (the long side). The diagonal is the hypotenuse of the right triangle.

Using the trigonometric function, we want to calculate the angle that the short side (8 cm) makes with the diagonal (hypotenuse). This is the angle opposite the 25 cm side.

We use the tangent function, which relates the angle of a right triangle to the ratios of its opposite side and adjacent side:

1. Identify the sides: Opposite side (to the angle) = 25 cm, Adjacent side = 8 cm.
2. Set up the equation using the tangent (tan) function: tan(θ) = opposite/adjacent = 25/8.
3. Solve for θ: θ = tan-1(25/8).
4. Use a calculator to find θ: θ ≈ 72.34°.

To the nearest degree, the angle is about 72°, which corresponds to option B.