In the MCDE diamond, the CE is 16 cm and the CDE is 120 degrees. Find the height of the diamond.
| January 6, 2021 | education
To solve the problem, we use the theorem of cosines and sines:
Consider a triangle EMC, in which the angle C is 120, EM = MC, and EC = 16 cm.
Find the sides EM and MC through the cosine theorem: EC = EM + MC – 2 * EM * CM * cos 120.
MS = EM = 16√3 / 3 cm.
The MED angle is 180 – 120 = 60.
Let’s lower the MO height.
In the triangle MOE, MO = 16√3 / 3 * cos 60 = 8 cm.
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