As seen from the top of the first tower, the angles of depression of the second tower's base and top are 56 degrees and 32 degrees, respectively.
dennis
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Let the first tower be CA(C at the bottom) and the second tower be BT(B at the bottom)
From your information angle BAC = 34 so BA = 100/sin 34
Also angle TAC = 58 so that AT = 100/sin 58.
We can now use the cosine rule on triangle BTA where angle BAT = 24 to get the height BT of the second tower
BT^2 = BA^2 + TA^2 - 2 BA*TA*cos 24.