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

(1 point)
Responses

20 mm
20 mm

11 mm
11 mm

10 mm
10 mm

7 mm

Answer 1

Triangles KLF and KMF are right with shared hypotenuse KF = 12. The side MF is opposite the 35° angle at K, so

MF = KF · sin 35° = 12 · sin 35° ≈ 12 · 0.5736 ≈ 6.89 mm ≈ 7 mm.

Answer: 7 mm.