Question

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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)
Responses

120 ft.
120 ft.

20 ft.
20 ft.

51 ft.
51 ft.

111 ft.

Answer 1

Because the radius to a tangent point is perpendicular to the tangent, triangle KFL is right at L. ∠LFK = 23° and KL = 47 ft is the side opposite that angle, so

FL = KL / tan(23°) = 47 / tan(23°) ≈ 110.7 ft ≈ 111 ft.

Answer: 111 ft.