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3 years ago

What is the measure of ∠E, rounded to the nearest degree? 28 36 54 80

Mathematics

1 answer:

katrin2010 [14]3 years ago

3 0

Answer: choice B) 36 degrees

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Work Shown:

Use the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
(DF)^2 = (EF)^2 + (DE)^2 - 2*(EF)*(DE)*cos(E)
6^2 = 10^2 + 7^2 - 2*10*7*cos(E)
36 = 100 + 49 - 140*cos(E)
36 = 149 - 140*cos(E)
36 - 149 = -140*cos(E)
-113 = -140*cos(E)
cos(E) = -113/(-140)
cos(E) = 0.80714285714286
E = arccos(0.80714285714286)
E = 36.1822872211523 <<--- see note below
E = 36 degrees

Note: arccos is the arccosine function, or the inverse cosine function. Make sure you are in degree mode

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3 years ago

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tino4ka555 [31]

Answer:

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3 years ago

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4 years ago

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4 years ago

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Rom4ik [11]

The slope of the line passing through points A and B is

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Since this line passes through (0, 3), its equation would be

y - 3 = (b + a) (x - 0) ==> y = (b + a) x + 3

It also passes through (-3/2, 0), so that

y - 0 = (b + a) (x + 3/2) ==> y = (b + a) x + 3/2 (b + a)

If these equations describe the same line, then they must have the same slope and y-intercept, so that

3 = 3/2 (b + a) ==> a + b = 2

It also passes through (a, a ²), so that

a ² = (b + a) a + 3 ==> a ² = ab + a ² + 3 ==> ab = -3

Solving for b in the first underlined equation, we get

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3 years ago