The base of the rectangular parallelepiped is a rhombus with a side of 8 cm, the acute angle of which is 60
| March 23, 2021 | education
The base of the rectangular parallelepiped is a rhombus with a side of 8 cm, the acute angle of which is 60 degrees. Find the length of the smaller diagonal of the parallelepiped if the height is 15 cm.
The smaller diagonal AC1 of the box ABCDA1B1C1D1 is the hypotenuse of the right triangle ACC1.
Let us find the length of the diagonal of the rhombus AC:
AC = 2 * 8 * cos60 ° = 1/2 * 2 * 8 = 8 cm.
Let us find the length of the diagonal of the parallelepiped AC1 by the Pythagorean tower.
AC1 = √ (8 ^ 2 + 15 ^ 2) = √289 = 17 cm.
Answer: the length of the smaller diagonal of the parallelepiped is 17 centimeters.
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