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Dmitry [639]
2 years ago
7

The diagram shows a 3 cm x 5 cm x 4 cm cuboid

Mathematics
1 answer:
Rainbow [258]2 years ago
4 0

Answer:

a) The length of segment AC is approximately 5.83 centimeters.

b) The angle ACD is approximately 34.5º.

Step-by-step explanation:

a) Since AB \perp BC, the length of segment AC is determined by Pythagorean Theorem, that is:

AC = \sqrt{(5\,cm)^{2}+(3\,cm)^{2}}

AC \approx 5.831\,cm

The length of segment AC is approximately 5.831 centimeters.

b) Since AB \perp BC \perp AD, the length of segment AD is determined by this Pythagorean identity:

AD = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}+(4\,cm)^{2}}

AD \approx 7.071\,cm

The angle ACD is determined by the following trigonometric expression:

\cos C = \frac{AC}{CD}

\cos C = \frac{5.831\,cm}{7.071\,cm}

\cos C = 0.825

C = \cos^{-1} 0.825

C \approx 34.448^{\circ}

The angle ACD is approximately 34.448º.

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