Answers:
- side DE = 16.1 units
- angle E = 60.3 degrees
- angle D = 29.7 degrees
The "units" and "degrees" portions of the answers are likely to be left out.
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Explanation:
Since we have a right triangle, we can use the pythagorean theorem to find the hypotenuse DE
a^2+b^2 = c^2
c = sqrt(a^2+b^2)
c = sqrt(8^2+14^2)
c = 16.124515496597
c = 16.1 is the approximate length of side DE
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We'll use the tangent ratio to find angle E
tan(angle) = opposite/adjacent
tan(E) = FD/FE
tan(E) = 14/8
E = arctan(14/8)
E = 60.2551187030578
E = 60.3 degrees
The notation arctan is the same as inverse tangent. You should have a [tex]\tan^{-1}[/tex] button on your calculator to help compute the inverse tangent.
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We could use the tangent ratio to solve for angle D, by noting that
tan(D) = 8/14
or we could use the idea that D+E = 90 which solves to D = 90-E
D = 90-E
D = 90-60.3
D = 29.7 degrees
Note how arctan(8/14) = 29.74488 which rounds to 29.7
