Update multiple records in table by using a reference table SQL Server

Question

I am trying to update a table in SQL by using references from two other tables. I need Table C to be updated with the ID of records from Table A but only where a column from Temp Table B exists in Table A

Table A

ID	ReferenceNumber
1	123
2	321
3	213
4	413

Temp Table B

ID	ExtractedNum
1	213
2	413
3	321
4	123

Expected Results

Table C

TableA_ID	TableB_ID
3	1
4	2
2	3
1	4

I've tried a few different queries but none of them work the way I need it to:

UPDATE table_c 
  SET
      table_c.tablea_id = a.id -- int    
FROM table_a a
WHERE table_c.tableb_id =
(
    SELECT t.Id, 
           t.ExtractedNum
    FROM #tempTableB t, 
         table_a a2  
    WHERE t.ExtractedNum = a2.ReferenceNumber
);

Answer 1

UPDATE c
SET c.tablea_id=a.id
FROM tableC c INNER JOIN
tableA a ON a.id=c.tablea_id INNER JOIN
#tempTableB b ON b.ExtractedNum=a.ReferenceNumber