Question

A vertical line connects upper K to upper F. Diagonal lines connect upper K with upper L and upper K with upper M. Similarly, the points upper L and upper F are connected via a diagonal line and the points upper M and upper F are connected via a diagonal line.

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¯¯¯¯¯¯¯¯¯¯
𝐾
𝑀
¯
and KL¯¯¯¯¯¯¯¯
𝐾
𝐿
¯
are tangent to the circle at L
𝐿
and M
𝑀
, ∠LFK=23 degrees
∠
𝐿
𝐹
𝐾
=
23

degrees
, and KM¯¯¯¯¯¯¯¯¯¯=47 feet
𝐾
𝑀
¯
=
47
feet
, how long is LF¯¯¯¯¯¯¯
𝐿
𝐹
¯
to the nearest foot?

(1 point)
Responses

20 ft.
20 ft.

111 ft.
111 ft.

120 ft.
120 ft.

51 ft.
51 ft.

Answer 1

Because FL is a radius and KL is tangent at L, FL ⟂ KL. So triangle KLF is right with ∠L = 90° and ∠LFK = 23°. The side KL = 47 ft is opposite the 23° angle, so

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

Rounded to the nearest foot: 111 ft.