Mast angles and height

Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast.

Final Answer:

h =  13.6558 m

Step-by-step explanation:

$$\begin{gathered} \alpha =11{}^{\circ } \\ \beta =28{}^{\circ } \\ {y}_1=10\text{m} \\ \tan \beta =y_1:x \\ x=y_1/\tan \beta =y_1/\tan 28°=10/\tan 28°=10/0.531709=18.80726\text{m} \\ \tan \alpha =y_2:x \\ {y}_2=x\cdot \tan \alpha =x\cdot \tan 11°=18.8073\cdot \tan 11°=18.8073\cdot 0.19438=3.65576\text{m} \\ h=y_1+y_2=10+3.6558=13.6558\text{m} \end{gathered}$$

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