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 result:

h =  13.1433 m

Solution:

c=50 m A=18 ∘ B=3⋅ A=3⋅ 18=54 ∘ A0=A∘→ rad=A∘⋅ π180 =18∘⋅ 3.1415926180 =0.31416=π/10 B0=B∘→ rad=B∘⋅ π180 =54∘⋅ 3.1415926180 =0.94248=3π/10 h/c1=tan⁡A h/c2=tan⁡B c=c1+c2 h/tan⁡A+h/tan⁡B=c  h=c/(1/tan⁡(A0)+1/tan⁡(B0))=50/(1/tan⁡(0.3142)+1/tan⁡(0.9425))=13.1433 m

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