Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. The diagonal of a rectangle is 354 millimeters, while the longer side is 274 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with the sides. Round the side length to the nearest millimeter. Round the angles to the nearest degree.
A)The side is 224 mm; the angles are 59° and 31°.
B)The side is 213 mm; the angles are 59 ° and 31 ° .
C)The side is 213 mm; the angles are 51 ° and 39 ° .
D)The side is 224 mm; the angles are 51 ° and 39 ° .
E)The side is 224 mm; the angles are 56 ° and 34 ° .

Question

Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. The diagonal of a rectangle is 354 millimeters, while the longer side is 274 millimeters. Find the shorter side of the rectangle and the angles the diagonal makes with the sides. Round the side length to the nearest millimeter. Round the angles to the nearest degree. ​
A)The side is 224 mm; the angles are 59° and 31°.
B)The side is 213 mm; the angles are 59 ° and 31 ° .
C)The side is 213 mm; the angles are 51 ° and 39 ° .
D)The side is 224 mm; the angles are 51 ° and 39 ° .
E)The side is 224 mm; the angles are 56 °  and 34 ° .

Quizplus · Accepted Answer

We can use the Pythagorean theorem to find the shorter side of the rectangle:
shorter side = √(diagonal² - longer side²) = √(354² - 274²) ≈ 224 mm

Next, we can use trigonometry to find the angles the diagonal makes with the sides of the rectangle. Let θ be one of the angles, then we have:
sin(θ) = (shorter side) / (diagonal) = 224 / 354 
θ ≈ 39°

So one angle is 39°, and the other angle is 90° minus this angle, which is approximately 51°. Therefore, the best choice is D.

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