Question

Use the image to answer the question.

A circle has center point upper F. The circumference point upper L is at the left of the circle and the circumference point upper M is at the right of the circle. Point upper K is above the circle in line with upper F.
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Identify and use the relationship between the radius and a line tangent to the circle, where the radius intersects the circle, to solve the following. If KM¯¯¯¯¯¯¯¯¯¯
and KL¯¯¯¯¯¯¯¯
are tangent to the circle at L
and M
, ∠LFK=23 degrees
, and KM¯¯¯¯¯¯¯¯¯¯=47 feet
, how long is LF¯¯¯¯¯¯¯
to the nearest foot?

(1 point)

111 ft.

120 ft.

51 ft.

20 ft.

Answer 1

KL = KM = 47 ft (tangents from the same external point). FL is perpendicular to KL, so triangle KFL is right with right angle at L. In that triangle, ∠F = 23° and the side opposite ∠F is KL, the side adjacent is LF. So

tan 23° = KL / LF => LF = KL / tan 23° = 47 / tan 23° ≈ 110.7 ft.

Rounded to the nearest foot: 111 ft.