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8090 [49]
3 years ago
7

In ΔBCD, the measure of ∠D=90°, BC = 81 feet, and DB = 52 feet. Find the measure of ∠C to the nearest tenth of a degree.

Mathematics
2 answers:
kenny6666 [7]3 years ago
7 0

Answer:

<em>39.9° </em>

Step-by-step explanation:

m∠C = β

sin β = \frac{52}{81} ⇒ β = arcsin \frac{52}{81} ≈ <em>39.9°</em>

Lyrx [107]3 years ago
7 0

Answer:

39.9

Step-by-step explanation:

sinC=  

sin C = \{52}{81}

sinC=  

81

52

​  

 

C=\sin^{-1}{52}{81})

C=sin  −1 (  81 /52 )

C=39.9393\ 39.9^

C=39.9393≈39.9∘

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To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of
postnew [5]

Answer:

The student's GPA for that term is 3.07

Step-by-step explanation:

So this is a problem where we need to compute a weighted arithmetic mean.

To compute the weighted arithmetic mean of a set, we need to multiply each value of the set by their respective weight, add them, and then divide by the sum of the weights.

I will write the set in a {V,W} way, where V is the value(the grade) and W is the weight of V.

So your set G will be

G = {{3.8, 5}, {1.8,3}, {3.1,5}, {3.1,5}}.

Multiplying each value by it's respective weigth and then adding, we have:

3.8*5 + 1.8*3 + 3.1*5 + 3.1*5 = 19 + 5.4 + 15.5 + 15.5 = 55.4

The sum of the weigths is 5 + 3 + 5 + 5 = 18

So the student's GPA for that term, rounded to two decimal places, is: 55.4/18 = 3.07

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Which terrorist group has been a major force in the conflicts in Iraq, Syria, and Yemen?
gizmo_the_mogwai [7]
D. Al- Qaeda
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Please answer this question its urgent
daser333 [38]
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There are 96 children in a room.
Olenka [21]

Answer:

7/12

Step-by-step explanation:

Basically to find the boys fraction I subtracted 40 from 96 and got 56. Your answer for the number of boys would be 56/96. I divided 4 from each and got 14/24. lastly I divide by 2 and got 7/12.

5 0
3 years ago
If 180° &lt; α &lt; 270°, cos⁡ α = −817, 270° &lt; β &lt; 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?
eduard

Answer:

cos(\alpha+\beta)=-\frac{84}{85}

Step-by-step explanation:

we know that

cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)

Remember the identity

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

step 1

Find the value of sin(\alpha)

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

cos(\alpha)=-\frac{8}{17}

Find the value of sine

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

substitute

(-\frac{8}{17})^{2}+sin^2(\alpha)=1

sin^2(\alpha)=1-\frac{64}{289}

sin^2(\alpha)=\frac{225}{289}

sin(\alpha)=-\frac{15}{17}

step 2

Find the value of cos(\beta)

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

sin(\beta)=-\frac{4}{5}

Find the value of cosine

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

substitute

(-\frac{4}{5})^{2}+cos^2(\beta)=1

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

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

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

step 3

Find cos⁡ (α + β)

cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)

we have

cos(\alpha)=-\frac{8}{17}

sin(\alpha)=-\frac{15}{17}

sin(\beta)=-\frac{4}{5}

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

substitute

cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})

cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}

cos(\alpha+\beta)=-\frac{84}{85}

4 0
3 years ago
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