What is the angle needed to solve this right triangle?

AI Thread Summary
The discussion revolves around solving a right triangle problem involving angles and side lengths. The user calculated the lengths of sides AB and CD using tangent functions but found a discrepancy with the textbook answer for CD, suspecting a typo in the angle measurement. Feedback from other participants confirmed the likelihood of a typo and provided a hint for finding the missing angle AEB by extending line AB. The calculations for AB and CD were deemed correct based on the provided angles. Clarification on the angle labels in the problem was also addressed, emphasizing the importance of accurate angle identification.
nmnna
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Homework Statement
In figure ##\angle{ABC} = 90^\circ = \angle{BCD}, \ \angle{ACB} = 41.45^\circ, \ \angle{CBD} = 32.73^\circ, \ BC = 10##cm. Calculate ##AB, \ CD## and ##\angle{AEB}##
Relevant Equations
##\tan{\alpha} = \frac{opposite \ side}{adjacent \ side}##
The Figure
1616228240588.png

My Attempt at Solution

##\tan{ACB} = \frac{AB}{BC}, \ \tan41.45^\circ = \frac{AB}{10} \Rightarrow AB = 10\tan45.41^\circ \approx 8.83##cm
Similarly
##\tan{CBD} = \frac{CD}{BC}, \ \tan32.73^\circ = \frac{CD}{10} \Rightarrow CD = 10\tan32.73^\circ \approx 6.43##cm
After this I checked the answer in my textbook, and instead of 6.43cm the answer for ##CD## was 4.40cm.
I thought that there was a typo in the problem, so instead of ##32.73^\circ##, I tried ##23.73^\circ##, and surprisingly the answer matches with the one in the textbook.
So I'd like to know if it really is a typo or my solution is wrong.
And I can't find the angle required in the problem, so I'd be grateful if you give me some hints for finding this angle.
 
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nmnna said:
Homework Statement:: In figure ##\angle{ABC} = 90^\circ = \angle{BCD}, \ \angle{BCD} = 41.45^\circ,
You have angle ##BCD## twice there. Please clarify.
 
PeroK said:
You have angle ##BCD## twice there. Please clarify.
It should be ##ACB##
 
nmnna said:
So I'd like to know if it really is a typo or my solution is wrong.
And I can't find the angle required in the problem, so I'd be grateful if you give me some hints for finding this angle.
Looks like a typo.

A hint to find the angle ##AEB##. First extend the line ##AB## to a new point, ##F##, so that ##AFD## is a right angle. Then you have another angle equal to ##AEB##.
 
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Your work is correct starting with the numbers you were given.
 
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