The base of a right prism is a rhombus with a side of 10 cm and an altitude of 9.6 cm. Find the diagonals of the prism if the altitude of the prism is 12 cm.

Answer 1

The diagonals of the prism are formed by the height of the prism, which is 12 cm, and the diagonals of the base rhombus.
I will do one of the diagonals , you do the other.

for acute angle of the rhomus:
sinØ = 9.6/10
Ø = 73.7°
the the obtuse angle is 106.3°

long diagonal of base:
x^2 = 10^2 + 10^2 - 2(10)(10)cos106.3°
= 256

(sines and cosines are exact values)

diagonal^2 = x^2 + 12^2 = 256+144 = 400
diagonal = √400 = 20