The lateral edge of the inclined prism is 16 cm and is inclined to the base plane at an angle of 60 degrees

The lateral edge of the inclined prism is 16 cm and is inclined to the base plane at an angle of 60 degrees. Find the height of the prism.

The lateral edge of the inclined prism AB, which is inclined to the base plane at an angle of 60 °, and the height of the prism AH, form a right-angled triangle ABН with a hypotenuse AB = 16 cm.Since one of the acute angles of this triangle is 60 °, the second is 30 °. And a right-angled triangle opposite an angle of 30 ° lies a leg equal to half of the hypotenuse, that is:

HB = 0.5AB = 8 cm.

Knowing the hypotenuse and leg, according to the Pythagorean theorem, we can find the height AH (aka the second leg):

AH = √ (AB² – HB²) = √ (16² – 8²) = √ (256 – 64) = √192 ≈ 14 cm.