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gulaghasi [49]
3 years ago
12

Can anybody tell me what’s going on here?

Mathematics
1 answer:
masha68 [24]3 years ago
7 0

Step-by-step explanation:

We are given a theta degree measure of sin in a specific interval. We are asked to find half of that degree measure.

The interval it ask us to find it in is between 2 pi and 5 pi over 2.

That is 360 degrees to 450 degrees. If you use reference angles, that is between the 0 degrees and 90 degrees. So that means our measure is going to be in the 1st quadrant.

Replace x with theta

\sin( \frac{x}{2} )   =  +  -   \sqrt{ \frac{1 -  \cos(x) }{2} }

We dont know cos x but we can use the pythagorean trig theorem to find cos x.

\sin {}^{2} (x)  +  \cos {}^{2} (x)  = 1

\sin {}^{2} ( \frac{4}{5} )  +  \cos {}^{2} (x)  = 1

\frac{16}{25}  +  \cos {}^{2} (x)  = 1

\cos {}^{2} (x)  = 1  -  \frac{16}{25}

\cos {}^{2} (x)  =  \frac{9}{25}

\cos(x)  =  \frac{3}{5}

Cosine in 1st quadrant is positive so 3/5 is cos x.

Replace 3/5 for cos x.

+  -   \sqrt{ \frac{1 -  \frac{3}{5} }{2} }

+  -  \sqrt{  \frac{2}{10}  }

The answer is

+  -  \sqrt{ \frac{2}{10} }

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C. 5.35

Step-by-step explanation:

Because the midsegment is half of the base

All you have to do is divide the 10.7 by 2

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Answer:

\large\boxed{\dfrac{15}{60}=\dfrac{5}{20}=\dfrac{3}{12}=\dfrac{1}{4}}

or

\large\boxed{\dfrac{15}{60}=\dfrac{30}{120}=\dfrac{45}{180}=\dfrac{60}{240}}

Step-by-step explanation:

Divide the numerator and the denominator by the same number:

\dfrac{15}{60}\\\\=\dfrac{15:5}{60:5}=\dfrac{3}{12}\\\\=\dfrac{15:3}{60:3}=\dfrac{5}{20}\\\\=\dfrac{15:15}{60:15}=\dfrac{1}{4}\\\vdots

or

Multiply the numerator and the denominator by the same number:

\dfrac{15}{60}\\\\=\dfrac{15\cdot2}{60\cdot2}=\dfrac{30}{120}\\\\=\dfrac{15\cdot3}{60\cdot3}=\dfrac{45}{180}\\\\=\dfrac{15\cdot4}{60\cdot4}=\dfrac{60}{240}\\\vdots

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3 years ago
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Given: <br> ΔABC, m∠C = 90º, m∠B = 30º<br> CM - angle bisector<br><br> Find: m∠AMC
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Answer:

75°

Step-by-step explanation:

1. Consider right triangle ABC. In this triangle

m∠C = 90º and CM - angle bisector.

If CM is angle C bisector, then

m∠ACM = m∠MCB = 45º

2. Consider triangle CMB. The sum of the measures of all interior angles of the triangle is always 180°, then

m∠MCB + m∠CBM + m∠BMC = 180°,

m∠BMC = 180° - 45° - 30°

m∠BMC = 105°

3. Angles AMC and BMC are supplementary angles, so

m∠AMC + m∠BMC = 180°

m∠AMC = 180° - 105°

m∠AMC = 75°

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3 years ago
Will someone please answer this and remind me how to solve this
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Step-by-step explanation:

Since the two triangles are similar, you can use proportions to solve for the value of x

\frac{x}{12}  = \frac{4}{3}

Now, just multiply 4 and 12.

4 * 12 = 48

Then divide that by 3.

48 / 3 = 16

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