Question

Identify and use the relationship between the radius and a line tangent to the circle, where the radiusintersects the circle, to solve the following. If
and
are tangent to the circle at
and
,
, and
, how long is
to the nearest foot?
(1 point)
K¯¯¯¯¯M¯¯¯¯¯ KL ¯¯¯¯¯¯¯¯ L M
∠LFK = 23 degrees KM = 47 feet ¯¯¯¯¯¯¯¯¯¯ LF ¯¯¯¯¯¯¯
51 ft.
111 ft.
20 ft.
120 ft

Answer 1

Because the radius to a point of tangency is perpendicular to the tangent, the segment LF and KM form a right triangle with angle ∠LFK = 23°. Thus

tan(23°) = LF / KM => LF = KM·tan(23°) = 47·tan(23°) ≈ 47·0.4245 ≈ 19.96.

Rounded to the nearest foot: 20 ft.