The base of the straight prism is a triangle with sides 5,5,6. The diagonal of the smaller side face

| June 29, 2021 | education

The base of the straight prism is a triangle with sides 5,5,6. The diagonal of the smaller side face makes an angle of 30 degrees with the base plane. Find the volume of the prism.

Since in the triangle ABC, AC = BC = 5 cm, then the triangle ABC is isosceles. Let’s build the height of CH to the base of AB. CH is also the median of the triangle ABC, then AH = BH = AB / 2 = 6/2 = 3 cm.

In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the leg CH.

CH ^ 2 = AC ^ 2 – AH ^ 2 = 25 – 9 = 16.

CH = 4 cm.

Determine the area of the base of the prism.

Sb = AB * CH / 2 = 6 * 4/2 = 12 cm2.

In a right-angled triangle AA1C tg30 = AA1 / AC.

AA1 = AC * tg30 = 5 * √3 / 3 cm.

Then V = Sosn * АА1 = 12 * 5 * √3 / 3 = 20 * √3 cm3.

Answer The volume of the prism is 20 * √3 cm3.



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