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NNADVOKAT [17]
3 years ago
9

*SAT QUESTION*

SAT
2 answers:
antoniya [11.8K]3 years ago
5 0

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

denis23 [38]3 years ago
3 0

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~DEF~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

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