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alexandr402 [8]
3 years ago
13

What is the area of this triangle?

Mathematics
2 answers:
MariettaO [177]3 years ago
8 0

the area of triangle with two sides and one angle is given by the formula

A= a.b.sin(x)/2, where x is the angle between a and b

so, for the given question,

A = 2.7*3.4*sin(40)/2

A= 2.905 feet^2

jonny [76]3 years ago
6 0
The answer 4.59 i really do hope i helped out have a great day.
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Help with this question.
pychu [463]

Answer:

angleS=83^o

angleR=23^o

Step-by-step explanation:

<h3><u>The Law of Sines</u></h3>

The Law of Sines states that for a given triangle (in a plane), the ratio formed by the Sine of any one of the three interior angles and the side across from it is equal to a common number.

If a triangle is drawn in standard form, with the three vertices identified as A, B, and C, and the interior angles at each vertex simply identified as angleA, angleB, angleC, the sides across from those angles are identified as a, b, and c, respectively.  Given such a labeling for a triangle, the Law of Sines gives the following equation:

\frac{sin(angleA)}{a} =\frac{sin(angleB)}{b} =\frac{sin(angleC)}{c}

From the picture you presented, with triangle RST, side r is on the right and unlabeled, side s is shown in red, and side T is shown in green.  The interior angles for R and S are unlabeled, and angle T is defined as 74 degrees.  The Law of Sines would give the following relationship for your triangle:

\frac{sin(angleR)}{r} =\frac{sin(angleS)}{s} =\frac{sin(angleT)}{t}

Substituting known values...

\frac{sin(angleR)}{r} =\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}

It should be noted that without information about the length of side r, angle R cannot be found directly with the Law of Sines because that portion of the equation holds two unknowns.  However, if the other two angles of the triangle are known, angle R can be solved for by using the Triangle Sum Theorem.

<h3><u>Finding Angle S</u></h3>

Focusing in on the ratio with known values on the far right, and the ratio containing angleS first:

\frac{sin(angleS)}{12.7ft} =\frac{sin(74^{o} )}{12.3ft}

... multiplying both sides of the equation by 12.7 ft...

sin(angleS) =\frac{sin(74^{o} ) * 12.7ft}{12.3ft}

Note that the right side of the equation has units of feet in both the numerator and denominator (with no addition or subtraction), so the units will cancel.  Simplifying the right side of the equation by evaluating the expression in a calculator (make sure you're in "degree" mode), will yield a unit-less number:

sin(angleS) = .9925222389...

Undoing the sine function, and solving for the measure of angle S will require taking the "arcsin" of both sides of the equation...

arcsin(sin(angleS))=arcsin(0.9925222389...)\\angleS=arcsin(0.9925222389...)\\angleS=82.98876661...^o\\angleS=83^o<u />

<u />

<h3><u>Finding Angle R</u></h3>

Knowing both angleS and angleT, we can apply the Triangle Sum Theorem to solve for angle R.

Triangle Sum Theorem:  The sum of all 3 interior angles in a triangle (in a plane) is 180 degrees.

angleR+angleS+angleT=180^o\\angleR+83^o+74^o=180^o

Using the subtraction property of equality to isolate angleR and combining like terms...

angleR=180^o-83^o-74^o\\angleR=23^o

8 0
2 years ago
5(x - 3) = 2(x + 6) + 3x
Verdich [7]
The first one is
5x-15=2x+12+3x
5x-2x-3x=12+15
0=27

The second one is
6.5x-7.75x=-12+14.5
-1.25x=-2.5
Divide both sides by - 1.25
X=. 02

The third one is
K-10=3
K=13
The second part of the third one is
-|k-10|=3
-k+10=3
-k=3+10
-k=13
Divide both sides by negative
K=-13

The fourth one is
4n+32=56
4n=56-32
4n=24
Divide both sides by 4
N=6
The second part to that one is
-4|n+8|=56
-4n-32=56
-4n=88
Divide both sides by - 4
N=22

The fifth one is
N+7-6=8
N=8-7+6
N=1+6
N=7
The second part to this one is
-|n+7|-6=8
-n-7-6=8
-n=8+7+6
-n=21
Divide both sides by negative
N=-21

The last one is
5x-7-3=9
5x=9+7+3
5x=19
Divide both sides by 5
X=19 over 5
The second part to this one is
-|5x-7|-3=9
-5x+7-3=9
-5x=9-7+3
-5x=5
Divide both sides by - 5
X=-1
I hope this helps you out.
3 0
3 years ago
Which two lines are parallel?
Delicious77 [7]
D. 1 and 2 is your answer
4 0
2 years ago
Ben measures the height of two bottles. one is 12 centimeters, and the other is 15 centimeters. in millimeters, what is the diff
IgorC [24]

One bottle has a height of 12 centimeters or 12 cm. Let us call this h1, so h1 = 12 cm

While the other bottle has a height of 15 centimeters or 15 cm. Let us call this h2, so h2 = 15 cm

 

The difference in height can be calculated by subtracting the smaller number from the bigger number, therefore:

difference in height = h2 – h1

difference in height = 15 cm – 12 cm

difference in height = 3 cm

 

We know that in 1 meter there is:

1 meter = 100 centimeters = 1000 millimeters

Therefore,

difference in height = 3 cm (1000 millimeters / 100 centimeters)

difference in height = 30 mm

6 0
3 years ago
Find the value of x​
andrew11 [14]
X=27

11x=16.5(18)
11x=297
x=27
8 0
3 years ago
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