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.

If ∠L≅∠M
∠
𝐿
≅
∠
𝑀
and both equal 90 degrees, ∠LKF=35
∠
𝐿
𝐾
𝐹
=
35
degrees, and KF=12
𝐾
𝐹
=
12
mm, then what is the length of MF
𝑀
𝐹
to the nearest millimeter?

(1 point)
Responses

11 mm
11 mm

20 mm
20 mm

7 mm
7 mm

10 mm
10 mm

Answer 1

7 mm

Reason: KF is the hypotenuse (12 mm) of a right triangle with ∠K = 35°. The side MF corresponds to the side opposite ∠K, so MF = 12·sin(35°) ≈ 12·0.574 = 6.89 ≈ 7 mm.