Question

Use the image to answer the question.

A line with arrow heads at both its ends tangentially intersects the circumference of a circle at a single marked point labeled upper F. The center of the circle is marked by point upper A, which connects to a separate circumference point: upper J.



If FI
is tangent to the circle A
at point F
, AF=28
mm, and ∠FAJ=39
degrees, then what is the measure of FI
?

(1 point)
Responses

23 mm
23 mm

35 mm
35 mm

21 mm
21 mm

14 mm

Answer 1

Since AF is a radius to the point of tangency, AF ⟂ FI. In right triangle AFI, ∠FAI = 39°, AF = 28, and FI is opposite that angle. So

FI = AF · tan(39°) = 28 · tan(39°) ≈ 22.7 ≈ 23 mm.

Answer: 23 mm.