Question 160690: In right triangle ABC, altitude CD is drawn to hypotenuse AB. If CD=6 and AD=9, find DB.
PLEASE HELP!, THANKS
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! 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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