In a regular quadrangular pyramid, the side of the base is 6 cm, the angle of inclination of the side face
| September 16, 2021 | education
In a regular quadrangular pyramid, the side of the base is 6 cm, the angle of inclination of the side face to the plane of the base is 60 degrees. find the side edge of the pyramid.
Since the pyramid is correct, ABCD is a square, and its side is 6 cm. In a right-angled triangle OO1H, the leg HO1 is half the length of AD. HO1 = AD / 2 = 3 cm. Angle O1OH = 180 – 90 – 60 = 30.
Leg HO1 lies opposite angle 30, then its length is equal to half the length of the OH hypotenuse. Then OH = HO1 * 2 = 3 * 2 = 6 cm.
From the right-angled triangle DНO, by the Pythagorean theorem, we define the hypotenuse OD.
OD ^ 2 = OH ^ 2 + DH ^ 2 = 6 ^ 2 + 3 ^ 2 = 36 + 9 = 45.
OD = √45 = 3 * √5 cm.
Answer: The length of the side rib is 3 * √5 cm.
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