Answer:
- AM = 12.87 cm
- CM = 8.578 cm
- OD = 23.66 cm
Explanation:
Since the figure is symmetrical, angle MOA will be half of angle BOA, so will be 130°/2 = 65°. The tangent ratio is useful here. It tells you ...
tan(MOA) = MA/OA
AM = OA·tan(MOA) = 6·tan(65°)
AM ≈ 12.87 . . . cm
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Similarly, ...
CM = 4·tan(65°)
CM ≈ 8.578 . . . cm
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The cosine ratio is useful for finding OD.
cos(MOA) = OA/OM
OM = OA/cos(MOA) = 6/cos(65°)
Similarly, ...
DM = 4/cos(65°)
The length we want is OD, so ...
OD = OM +DM = 6/cos(65°) +4/cos(65°) = 10/cos(65°)
OD ≈ 23.66 . . . cm