RT with rectangle

In the diagram, find the lengths h and b.
One rectangle and one right triangle share one side. We know two angles and the length of the common side, as shown in the picture.

Final Answer:

h =  10.679 m
b =  29.6512 m

Step-by-step explanation:

$$\begin{gathered} a=20\text{m} \\ \alpha =28.1{}^{\circ } \\ \beta =56{}^{\circ } \\ \tan \alpha =h:a \\ h=a\cdot \tan \alpha =a\cdot \tan 28.1°=20\cdot \tan 28.1°=20\cdot 0.53395=10.679=10.679\text{m} \end{gathered}$$

$$\begin{gathered} \tan \beta =b:a \\ b=a\cdot \tan \beta =a\cdot \tan 56°=20\cdot \tan 56°=20\cdot 1.482561=29.651=29.6512\text{m} \end{gathered}$$

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