The lateral edge of the straight prism is 7 cm, and one of its diagonals is 14 cm.
| February 3, 2021 | education
The lateral edge of the straight prism is 7 cm, and one of its diagonals is 14 cm. Find the angle between the diagonal and the base plane.
According to the condition, we will consider a right-angled triangle, in which the lateral edge of the straight line of the prism is the leg, the diagonal is the hypotenuse, and the sought angle is the angle opposite to the lateral edge.
Calculation formula: sinα = l1 / L and α = arcsin (l1 / L), where l1 is the length of the lateral rib, leg (l1 = 7 cm); L – the length of the diagonal, hypotenuse (L = 14 cm).
Let’s calculate: α = arcsin (l1 / L) = arcsin (7/14) = arcsin 1/2 = 30º.
Answer: The required angle between the diagonal of the taken straight line of the prism and the plane of its base is 30º.
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