Tā késou le hǎojǐtiān, zhōngyú kǎ chū le yìxiē tán.
He had been coughing for several days and finally hacked up some phlegm.
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As kǎ this is a clinical/medical verb - mostly seen in 咯血 (hemoptysis) and 咯痰 (expectorate phlegm). The same character is also read luò in the chemistry term 吡咯 (pyrrole, C₄H₅N) - both readings are filed under one entry in older dictionaries.
mistakes
Don't confuse 咯 (hack up, throat-forced) with 咳 (to cough). 咳 is the cough itself; 咯 is what comes out of the cough - phlegm or blood. Doctors will ask about both.
Left radical 口 - semantically tight here: kǎ is a throat-forced expulsion through the mouth. Same radical pattern as 咳 (cough) and 吐 (spit), all clinical mouth-action verbs.
Right phonetic 各 - sound has drifted considerably (gè → kǎ, also luò in 吡咯). The k- initial preserves the velar stop from older readings of the 各 phonetic series; compare 客 which keeps the same k- onset.
