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Draw a horizontal line from Q to the flagpole. Label the intersection S.
The height of the pole is thus 20+ST
since
SQ/ST = cot25
SQ/(ST+20) = cot65
equate and solve for ST
Now you can get SQ
PT^2 = SQ^2 + (ST+20)^2
QT^2 = SQ^2 + ST^2