Tree

Between points A and B is 50m. From A, we see a tree at an angle of 18°. From point B, we see the tree at a three times bigger angle. How tall is a tree?

Correct answer:

h =  13.1433 m

Step-by-step explanation:

$$\begin{gathered} c=50\text{m} \\ A=18{}^{\circ } \\ B=3\cdot A=3\cdot 18=54{}^{\circ } \\ {A}_0=A°\to \text{rad}=A°\cdot \frac{\pi }{180}=18°\cdot \frac{3.1415926}{180}=0.31416=\pi /10 \\ {B}_0=B°\to \text{rad}=B°\cdot \frac{\pi }{180}=54°\cdot \frac{3.1415926}{180}=0.94248=3\pi /10 \\ h/c_1=\tan A \\ h/c_2=\tan B \\ c=c_1+c_2 \\ h/\tan A+h/\tan B=c \\ h=c/(1/\tan (A_0)+1/\tan (B_0))=50/(1/\tan 0.3142+1/\tan 0.9425)=13.1433\text{m} \end{gathered}$$

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