Tree

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

Correct answer:

h =  13.1433 m

Step-by-step explanation:

$$\begin{gathered} c=50\text{ m } \\ A=18\text{ ° } \\ B=3\cdot A=3\cdot 18=54\text{ ° } \\ {A}_0=A\mathrm{°}\to \text{ rad}=A\mathrm{°}\cdot {\displaystyle \frac{\pi }{180}}=18\mathrm{°}\cdot {\displaystyle \frac{3.1415926}{180}}=0.31416=\pi \mathrm{/}10 \\ {B}_0=B\mathrm{°}\to \text{ rad}=B\mathrm{°}\cdot {\displaystyle \frac{\pi }{180}}=54\mathrm{°}\cdot {\displaystyle \frac{3.1415926}{180}}=0.94248=3\pi \mathrm{/}10 \\ h\mathrm{/}{c}_1=\tan A \\ h\mathrm{/}{c}_2=\tan B \\ c=c_1+c_2 \\ h\mathrm{/}\tan A+h\mathrm{/}\tan B=c \\ h=c\mathrm{/}(1\mathrm{/}\tan (A_0)+1\mathrm{/}\tan (B_0))=50\mathrm{/}(1\mathrm{/}\tan (0.3142)+1\mathrm{/}\tan (0.9425))=13.1433\text{ m} \end{gathered}$$

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