Question

*SAT QUESTION*

Answer 1

Answer:

0.6

Explanation:

Angle F corresponds to Angle C

sinF = sinC

AC² = AB² + BC²

20² = AB² + 16²

AB² = 400 - 256

AB² = 144

AB = 12

sinC = AB/AC

sinC = 12/20

sinF = 0.6

Answer 2

Answer and Explanation:

$Greetings!$

$Let's~answer~your~question!$

$Triangle~ ABC ~is ~a ~right~ triangle~ with ~its~ right~ angle ~at ~B. ~Therefore,~AC\\is~ the~ hypotenuse~ of~ right~ triangle~ ABC,~ and~ AB ~and ~BC ~are~ the~ legs~ of~ right~\\ triangle ~ABC.$

$According~ to~ the~ Pythagorean ~theorem,$

$AB=\sqrt{20^2-16^2}=\sqrt{400-256}=\sqrt{144}=12$

$Since ~triangle~DE$$F~is ~similar~ to~ triangle~ ABC,~ with~ vertex ~F ~corresponding~to~ vertex~ C,~ the~ measure\\ of~angle~ \angle F~equals~ the~ measure~ of~ angle~\angle C.$

$Therefore,~ sinF=sinC. ~From ~the~ side~ lengths~ of ~triangle~ ABC,$

$sinF=\frac{opposite ~side}{hypotenuse} =\frac{AB}{AC} =\frac{12}{20}=\frac{3}{5}$

$Therfore, ~sinF=\frac{3}{5}~or~0.6$