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3 years ago

Explain why using the law of sines when given SSA information can result in one, two, or no triangles.

Mathematics

2 answers:

dem82 [27]3 years ago

6 0

Answer:

Step-by-step explanation:

Whenever SSA information is given, we have

a/sinA = b/sin B = c/sin C

When we know a and sin A, and b we can solve for sin B.

When sin B is known, we can have B take two values one in the I quadrant less than 90 and one in the ii quadrant more than 90.

Sometimes both angles have to be taken as solutions for two triangles.

In these cases, we can get two triangles as solution for the given information.

For example, if A =20 degrees and if we get sinB=1/2 then we can have B as either 30 or 150 since both consistent when added with 20 gives less than 180

In these cases we get two triangles as solution.

If A = 40 say then we can have B only taking 30.

In this case one solution.

No triangle is possible only when sum of two sides exceed third side in other words the given information do not form a triangle.

coldgirl [10]3 years ago

5 0

Due to the ambiguous case of the law of sines, two different triangles could be created. There may be a second angle if you are given two sides and the angle not in between. The ambiguous case may result in one solution, two solutions or no solutions therefore there can be one, two or no triangles.

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Tom has a piece of wood that is 10 and 1/3 inches long. He divides the wood into pieces that are 2 and 1/5 inches long. How many

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Find slope for 2x+5y=8?

Nitella [24]

First thing, you need to transform this equation to the form of y = ax + b

So you get:
2x + 5y = 8
5y = -2x + 8
$y = -\frac{2}{5} x + \frac{8}{5}$

In the form of y = ax + b, a is the slope.
In $y = -\frac{2}{5} x + \frac{8}{5}$ , you can see " $- \frac{2}{5} x$ ", and always the number before x is the slope
So, the slope of 2x + 5y = 8 is $- \frac{2}{5}$

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7 0

3 years ago

Read 2 more answers

Find the sum or difference <br> 1/2 - 1/14<br> A.3/7<br> B.2/7<br> C.4/7

pogonyaev

Answer:

A.3/7

Step-by-step explanation:

1/2 - 1/14

We need to get a common denominator of 14

1/2 * 7/7 = 7/14

7/14 - 1/14 = 6/14

We can simplify by dividing the top and bottom by 2

3/7

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3 years ago

s(t) = 0.29t2 − t + 25 gallons per year (0 ≤ t ≤ 7), where t is time in years since the start of 2007. Use a Riemann sum with n

Sav [38]

Answer: The answer is 300 gallons.

Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.

To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ $x_{k}$ = $\frac{b-a}{n}$

If a function is defined on the closed interval [a,b] and $c_{k}$ is any point in [ $x_{k-1}$ , $x_{k}$ ], then a Riemann Sum is defined as ∑f( $c_{k}$ )Δ $x_{k}$ .

For this question:

Δ $x_{k}$ = $\frac{7-0}{5}$ = 1.4

Now, we have to find s(t) for each valor on the interval:

s(t) = 0.29 $t^{2}$ - t +25

s(0) = 25

s(1) = 24.29

s(2) = 24.16

s(3) = 24.61

s(4) = 25.64

s(5) = 27.25

s(6) = 29.44

s(7) = 32.21

Now, using the formula:

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)

∑f( $c_{k}$ )Δ $x_{k}$ = 1.4(212.6)

∑f( $c_{k}$ )Δ $x_{k}$ ≅ 300

With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.

3 0

3 years ago