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kumpel [21]
3 years ago
7

Marty is asked to draw triangles with side lengths of 4 units and 2 units, and a non-included angle of 30°. Select all the trian

gles that he could have drawn. *

Mathematics
1 answer:
777dan777 [17]3 years ago
4 0

Answer:

The drawn in the attached figure

see the explanation

Step-by-step explanation:

<em>First case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\B=30^o

Applying the law of sines

Find the measure of angle A

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(A)}=\frac{2}{sin(30^o)}

sin(A)=1

so

A=90^o

Find the measure of angle C

In a right triangle

we know that

B+C=90^o ----> by complementary angles

B=30^o

therefore

C=60^o

Find the length side c

Applying the law of sines

\frac{c}{sin(C)}=\frac{b}{sin(B)}

substitute the given values

\frac{c}{sin(60^o)}=\frac{2}{sin(30^o)}

c=2\sqrt{3}\ units

therefore

The dimensions of the triangle are

A=90^o

B=30^o

C=60^o

a=4\ units\\b=2\ units\\c=2\sqrt{3}=3.46\ units

<em>Second case</em>

In the triangle ABC

Let

a=4\ units\\b=2/ units\\A=30^o

Applying the law of sines

Find the measure of angle B

\frac{a}{sin(A)}=\frac{b}{sin(B)}

substitute the given values

\frac{4}{sin(30^o)}=\frac{2}{sin(B)}

sin(B)=0.25

so

using a calculator

B=14.48^o

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180^o

A=30^o\\B=14.48^o

therefore

30^o+14.48^o+C=180^o

C=135.52^o

Find the length side c

Applying the law of sines

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

substitute the given values

\frac{c}{sin(135.52^o)}=\frac{4}{sin(30^o)}

c=5.61\ units

therefore

The dimensions of the triangle are

A=30^o

B=14.48^o

C=135.52^o

a=4\ units\\b=2\ units\\c=5.61\ units

see the attached figure to better understand the problem

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tamaranim1 [39]

Answer:

a) See the file below, b) s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx, c) s \approx 9.715

Step-by-step explanation:

a) Points moves clockwise as t increases. See the curve in the file attached below. The parametric equations describe an ellipse.

b) The arc length formula is:

s = \int\limits^{0.5\pi}_{-0.25\pi} {[\left( 3\cdot \cos t\right)^{2}+\left(-5\cdot \sin t \right)^{2}]} \, dx

c) The perimeter of that arc is approximately:

s \approx (\frac{1}{4} + \frac{1}{8})\cdot 2 \pi\cdot \sqrt{\frac{3^{2}+5^{2}}{2} }

s \approx 9.715

5 0
3 years ago
Choose the correct simplification of the expression (−2x + 4y)(3x − 7y).
Rudik [331]
-2x • 3x = -6x2 (the 2 is an exponent)
4y • -7y = -28y2 (the 2 is an exponent)
-2x • -7y = 14xy
4y • 3x = 12xy
14xy + 12xy = 26xy

—> -6x2(expo) - 28y2(expo) + 26xy

Check the answer again just to be sure, it’s been a while since I’ve had algebra!
3 0
3 years ago
what is the equation of the line that is parallel to 6x-2y=4+6y and passes through the point (8, -16)?
Alisiya [41]

Answer:

y=\frac{3}{4}x-22

Step-by-step explanation:

We are given;

  • The equation of a line 6x-2y=4+6y
  • A point (8, -16)

We are required to determine the equation of a line parallel to the given line and passing through the given point.

  • One way we can determine the equation of a line is when we are given its slope and a point where it is passing through,

First we get the slope of the line from the equation given;

  • We write the equation in the form y = mx + c, where m is the slope

That is;

6x-2y=4+6y

6y + 2y = 6x-4

8y = 6x -4

We get, y = 3/4 x - 4

Therefore, the slope, m₁ = 3/4

But; for parallel lines m₁=m₂

Therefore, the slope of the line in question, m₂ = 3/4

To get the equation of the line;

We take a point (x, y) and the point (8, -16) together with the slope;

That is;

\frac{(y--16}{x-8}=\frac{3}{4}

4(y+16)=3(x-8)\\4y + 64 = 3x - 24\\4y=3x-88\\ y=\frac{3}{4}x-22

Thus, the equation required is y=\frac{3}{4}x-22

4 0
3 years ago
PLS HELP ASAP
loris [4]
The percent of change is 73.33 percent
4 0
3 years ago
Can 5, 6 and 30 squared form a right triangle?
Galina-37 [17]

Answer:

no

Step-by-step explanation:

A triangle is equal to 180.

5²+6²=30²

25+36=900

61=900

No solution

4 0
3 years ago
Read 2 more answers
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