Apole tilts toward the sun at a 12° angle from the vertical, and it casts a 20-foot shadow. the angle of elevation from the tip of the shadow to the top of the pole is 36°. what is the length of the pole? round your answer to the nearest tenth. a) 4.5 ft b) 7.1 ft c) 11.8 ft d) 17.6 ft

The correct answer is option C) 11.8 ft

Step-by-step explanation:

From the figure attached with this answer shows the pictorial representation of the given scenario.

AB be the pole. pole tilts toward the sun at a 12° angle from the vertical shows AC.

ΔAEC and ΔDEC are two right angled triangle.

By using trigonometric ratios,

tan78 = x/y

x = y *tan(78) (1)

tan(36) = x/(20 - y)

x = (20 - y )*tan(36)    (2)

from (1) and (2) we get,

y *tan(78)  = (20 - y )*tan(36)

y*4.7  = 20*0.72 - y*0.72

5.42y = 14.4

y = 2.67 ft

To find x

x = y *tan(78)  = 2.67 * 4.7 = 12.56 ft

To find height of pole AC

cos(78) = y/AC

AC = y*cos(78) = 2.67 * 0.208 = 12.74ft

Therefore the correct answer in the given options is C) 11.8 ft

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step-by-step explanation: