<PRE><B>Question 160690</B>
you need to find angle DCA which will allow you to find angle DCB which will allow you to find DB.
you know that CD is 6 and you know that AD is 9.
tangent of DCA equals AD / CD = 9/6 = 1.5
arctangent of 1.5 = 56.30993247 degrees = DCA
DCA = 56.30993247 degrees.
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since ACB is a right angle, then angle DCB = 90 degrees minus DCA = 90 degrees minus 56.30993247 degrees = 33.69006753 degrees.
DCB = 33.69006753 degrees.
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tangent of DCB is BD / CD.
since CD is 6, tangent of DCB is BD / 6.
multiplying both sides of the equation by 6 and it becomes
BD = 6 * tangent of DCB = 6 * tangent of 33.69006753 degrees.
solving, BD becomes 4.
BD = 4.
BD and DB are the same line.
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answer is DB = 4.
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i solved for BC and for AC to get the other 2 sides of the triangle and then solved for c^2 = a^2 + b^2 to prove the answer was correct and it was confirmed.





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