Observer

The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 102 m.

How far is it from the another end of the fence?

Correct result:

x =  119.9 m

Solution:

sin⁡βsin⁡30∘=10260 β=arcsin⁡(10260⋅sin⁡30∘)=1.016=58∘12′42" γ=180∘−30∘−58∘12′42"=91∘47′18"  sin⁡γsin⁡β=x102 x=102⋅sin⁡γsin⁡β=119.9 m\dfrac{ \sin \beta} { \sin 30 ^\circ } = \dfrac{ 102 } { 60 } \ \\ \beta = \arcsin ( \dfrac{ 102 } { 60 } \cdot \sin 30 ^\circ ) = 1.016 = 58^\circ 12'42" \ \\ \gamma = 180 ^\circ - 30 ^\circ - 58^\circ 12'42" = 91^\circ 47'18" \ \\ \ \\ \dfrac{ \sin \gamma} { \sin \beta } = \dfrac{ x } { 102 } \ \\ x = 102 \cdot \dfrac{ \sin \gamma} { \sin \beta } = 119.9 \ \text{m}

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