Asked by Mark
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.
Answers
Answered by
Reiny
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
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
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