Angle of elevation

From a point A on the ground, the angle of elevation of the top of a 20 m tall of a building is 45°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is 60°. Find the length of the flagstaff and the distance of the building from the point A .

Correct answer:

l =  14.641 m
x =  20 m

Step-by-step explanation:

$$\begin{gathered} h=20\text{m} \\ \alpha =45{}^{\circ } \\ \beta =60{}^{\circ } \\ \tan \alpha =h:x \\ x=\frac{h}{\tan \alpha }=\frac{h}{\tan 45°}=\frac{20}{\tan 45°}=\frac{20}{1}=20\text{m} \\ \tan \beta =(h+l):x \\ x\cdot \tan \beta =h+l \\ l=x\cdot \tan \beta -h=x\cdot \tan 60°-h=20\cdot \tan 60°-20=20\cdot 1.732051-20=14.641=14.641\text{m} \end{gathered}$$

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