When the angle of elevation of the sun is 64°, a pole that is tilted at an angle of 19° directly away from the sun casts a shadow 21 feet long on level ground. approximate the length of the pole to the nearest foot?

Length of the pole is 27ft. ( rouding up to the nearest foot)

Explanation:

To solve this problem you need to understand that the the shadow cast by the pole on the ground connected to the pole itself and to the imaginary line of sun light forms a triangle with 3 different angles, please see the drawing to a better understanding.

* The sum of the internal angles of any triangle must be 180° then;

α: angle of the elevation of the sun= 64°

angle of the pole to the ground= (90-19)= 71°

β = 180 - ( 64+71) = 45°

*To find the length of the pole we can use the law of Sines;

|BC| / sin (α) = |AC| / sin (β)

|BC|= Length of the pole

|AC|= shadow of the pole on the ground which is known to be 21 ft

|BC| / sin (64°) = 21 / sin (45°)

|BC|= 21 x [sin (64°)/ sin (45°)]

|BC|= 21 x 1.27≅ 26.67 ft

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the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.