Mast shadow

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.

Result

x =  11.519 m

Solution:

s=13 m A=9015=75  B=9033=57  C=180AB=1807557=48   sinC:sinB=x:s  x=s sin(C rad)/sin(B rad)=s sin(C π180 )/sin(B π180 )=13 sin(48 3.1415926180 )/sin(57 3.1415926180 )=11.51928=11.519 ms=13 \ \text{m} \ \\ A=90 - 15=75 \ ^\circ \ \\ B=90 - 33=57 \ ^\circ \ \\ C=180 - A - B=180 - 75 - 57=48 \ ^\circ \ \\ \ \\ \sin C : \sin B=x: s \ \\ \ \\ x=s \cdot \ \sin( C ^\circ \rightarrow\ \text{rad} ) / \sin( B ^\circ \rightarrow\ \text{rad} )=s \cdot \ \sin( C ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) / \sin( B ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=13 \cdot \ \sin( 48 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) / \sin( 57 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=11.51928=11.519 \ \text{m}

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