# 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:

$s = 13 \ m \ \\ A = 90 - 15 = 75 \ ^\circ \ \\ B = 90 - 33 = 57 \ ^\circ \ \\ C = 180 - A - B = 180 - 75 - 57 = 48 \ ^\circ \ \\ \ \\ \sin C : \sin B = x: s \ \\ \ \\ x = s \cdot \ \sin( (C \rightarrow rad) = s \cdot \ \sin( C ) / \sin( (C \cdot \ \dfrac{ \pi }{ 180 } \ ) = 11.5192819451 ) / \sin( (B \rightarrow rad) = s \cdot \ \sin( C ) / \sin( (B \cdot \ \dfrac{ \pi }{ 180 } \ ) = 11.5192819451 ) = 11.519 \ \text { m }$

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Do you want to convert length units? See also our right triangle calculator. See also our trigonometric triangle calculator.

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