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For the triangle shown, find ∠BCD and ∠DCA.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
The unknown angles of two adjacent triangles can be solved by using Sine Law.
Consider ΔABC:
Use Sine Law in order to solve for ∠ABC, we have
Consider ΔBCD:
Since BC ≅ CD = 20, then it follows that ΔBCD is an isosceles triangle. If the two sides of an isosceles triangle are equal, then the two base angles are equal also. In this case,
∠DBC ≅ ∠CDB = 44.427°. Therefore,
Consider ΔACD:
Since ∠BDC and ∠ADC are supplementary angles, then we can solve for ∠ADC as follows
Therefore,
