SOLUTION: in triangle DEF, e= 3.0 cm angle F = 64 angle E 46 find the measurement of d

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Question 621531: in triangle DEF, e= 3.0 cm
angle F = 64
angle E 46
find the measurement of d
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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STEP I: Use the Angel Sum Theorem to find the measure of angle D.
The sum of the interior angles of any triangle is 180 degrees.
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[measure of angle D] + measure of angle E] + [measure of angle F] = 180 degrees
[measure of angle D] + 46 + 64 = 180
[measure of angle D] = 180 - 46 - 64 = 70
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The measure of angle D is 70 degrees.
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STEP II: Use the Law of Sines to find the length of d.
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The Law of Sines says the the following rations are equivalent.
sin%28D%29%2Fd=sin%28E%29%2Fe=sin%28F%29%2Ff
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We will use the first equivalence. Substitute the values you know and solve for d.
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sin%28D%29%2Fd=sin%28E%29%2Fe
sin%2870%29%2Fd=sin%2846%29%2F3
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Use a calculator to find values for the sine for each angle.
0.9397%2Fd=0.7193%2F3
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Solve for d.
d=%28%280.9397%29%283%29%29%2F%280.7193%29
d=3.92+cm%29
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Hope this helps! Please email if there is any part of this that does not make sense yet.
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Ms.Figgy
math.in.the.vortex@gmail.com