The height in feet of the portion AB of the lamppost is 20 tan 55° feet. The third option is correct.
The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;
sine, cosine and tangent.
The bent lamppost forms a right triangle ABC so that we evaluate for the height AB as follows:
tan 55° = AB/BC {opposite/adjacent}
tan 55° = AB/20
AB = 20 × tan 55° {cross multiplication}
Therefore, using the trigonometric ratio of tangent for the angle 55° at C, the height of the side length AB is equal to 20 tan 55° feet.