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Consider a Triangle ABC like the one below. Suppose that C = 98, A = 74, and b = 11 (figure is not drawn to scale.) solve the tr

Degger [83]

Answer:

$A=73.8\°$

$B=8.2\°$

$c=76.3\ units$

Step-by-step explanation:

step 1

Find the measure of side c

Applying the law of cosines

$c^{2}= a^{2}+b^{2}-2(a)(b)cos(C)$

substitute the given values

$c^{2}= 74^{2}+11^{2}-2(74)(11)cos(98\°)$

$c^{2}=5,823.5738$

$c=76.3\ units$

step 2

Find the measure of angle A

Applying the law of sine

$\frac{a}{sin(A)}=\frac{c}{sin(C)}$

substitute the given values

$\frac{74}{sin(A)}=\frac{76.3}{sin(98\°)}$

$sin(A)=(74)sin(98\°)/76.3$

$A=arcsin((74)sin(98\°)/76.3)$

$A=73.8\°$

step 3

Find the measure of angle B

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

$A+B+C=180\°$

substitute the given values

$73.8\°+B+98\°=180\°$

$171.8\°+B=180\°$

$B=180\°-171.8\°=8.2\°$

5 0

3 years ago

8

blagie [28]

Answer:

The new function is g(x) = x² +1

Step-by-step explanation:

Explanation:-

Given that the function f(x) = x²

From graph ,

The parabola y = x² is shifting to up with '1' units

y = x² +1

The new function is g(x) = x² +1

Verification:-

y = x²+1

Put x=0 ⇒ y =1

The point (0,1) lies on the parabola y = x²+1

similarly put x =1 and y = 2

The Point (1,2) lies on the Parabola y = x²+1

∴ The new graph y = x²+1

3 0

3 years ago

Solve 2x + 4 > 16 A. x > 10 B. x < 6 C. x < 10 D. x > 6

Salsk061 [2.6K]

Hey there! :)

2x + 4 > 16

We're simply just trying to get x onto it's own side, so let's get rid of any numbers on the same side of it.

We can start out by subtracting both sides by 4.

2x + 4 - 4 > 16 - 4

Simplify.

2x > 12

Then, divide both sides by 2.

2x ÷ 2 > 12 ÷ 2

Simplify.

x > 6

Therefore, our answer is D. x > 6

~Hope I helped!~

6 0

3 years ago

Find Mean, Median, mode and range. Round to the nearest tenth.

stiv31 [10]

Answer:

Mean = 26.24

Median = 27

Mode = 32

Range = 38

Step-by-step explanation:

Plotting the original data from leaf plot

$9,11,12,12,14,17,25,25,27,32,32,32,33,35,41,42,47$

Finding Mean:

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$\mu=\frac{446}{17}$

= 26.24

Therefore, the range = 26.24.

Finding Median:

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

So, the median is 27 .

Finding Mode:

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

We see that the mode is 32.

Finding Range:

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

9 11 12 12 14 17 25 25 27 32 32 32 33 35 41 42 47

The lowest value is 9.

The highest value is 47.

The range = 47 - 9 = 38

4 0

3 years ago

The width of a rectangle is 80 feet. The length of the rectangle is longer than the width by a distance of feet. Write an algebr

Sauron [17]

Length=width+x
l=w+x (x being the amount of feet longer than the width)

5 0

3 years ago

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