\(
\eqalign{
& \frac{h}
{{\tan (60)}} + \frac{h}
{{\tan (40)}} = 120 \cr
& \frac{{\tan (40) \cdot h}}
{{\tan (60) \cdot \tan (40)}} + \frac{{\tan (60) \cdot h}}
{{\tan (60) \cdot \tan (40)}} = 120 \cr
& \frac{{\tan (40) \cdot h + \tan (60) \cdot h}}
{{\tan (60) \cdot \tan (40)}} = 120 \cr
& \frac{{\left( {\tan (40) + \tan (60)} \right) \cdot h}}
{{\tan (60) \cdot \tan (40)}} = 120 \cr
& \left( {\tan (40) + \tan (60)} \right) \cdot h = 120 \cdot \tan (60) \cdot \tan (40) \cr
& {\text{h = }}\frac{{120 \cdot \tan (60) \cdot \tan (40)}}
{{\tan (40) + \tan (60)}} \approx 67,8 \cr}
\)
