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3 years ago

Based on the given angle measures, which triangle has side length measures that could be correct?

Mathematics

2 answers:

Likurg_2 [28]3 years ago

8 0

Answer

The triangle in the figure 4 is correct .

Reason

by using the trignometric identity

$tan\theta = \frac{Perpendicular}{Base}$

Thus

$tan 30^{\circ} = \frac{Perpendicular}{Base}$

$tan 30 ^{\circ} =\frac{1}{\sqrt{3}}$

Now in the figure (1)

$tan 30^{\circ} = \frac{13.9}{8}$

$\frac{1}{\sqrt{3}} = \frac{13.9}{8}$

on simplify

$0.5774 \neq 1.7375$

thus side length measures in the figure (1) is not correct .

Now in the figure (2)

$tan30^{\circ} =\frac{16}{8} \\ \frac{1}{\sqrt{3}} =\frac{16}{8} \\ 0.577 \neq 2$

thus side length measures in the figure (2) is not correct .

Now in the figure (3)

$tan 30 ^{\circ} = \frac{8}{16} \\ \frac{1}{\sqrt{3}} =\frac{8}{16} \\ 0.577\neq0.5$

thus side length measures in the figure (3) is not correct .

Now in the figure (4)

$tan30^{\circ} = \frac{8}{13.9} \\ \frac{1}{\sqrt{3}} =\frac{8}{13.9}\\ 0.577 = 0.576(approx)$

Therefore the figure (4) is correct triangle has side length measures that could be correct

Hence proved

Phoenix [80]3 years ago

8 0

Answer:

The answer is D on edgen.

Step-by-step explanation:

D. the 4th figure

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Suppose that ? Is an angle with csc(?)=-12/5 and ? Is not in the third quadrant. Compute the exact value of Tan(?). You don’t ha

Damm [24]

Answer:

$tan(\theta)=-\frac{5}{\sqrt{119}}$

Step-by-step explanation:

The correct question is

Suppose that ∅ Is an angle with csc(∅)=-12/5 and ∅ Is not in the third quadrant. Compute the exact value of Tan(∅).

∅ Is not in the third quadrant

If csc(∅) is negative the angle lie in the III Quadrant or in the IV Quadrant

∅ Is not in the third quadrant ----> given problem

That means ----> ∅ Is in the fourth quadrant

step 1

Find the value of $sin(\theta)$

we have

$csc(\theta)=-\frac{12}{5}$

we know that

$csc(\theta)=\frac{1}{sin(\theta)}$

therefore

$sin(\theta)=-\frac{5}{12}$

step 2

Find the value of $cos(\theta)$

we know that

$sin^2(\theta)+cos^2(\theta)=1$

we have

$sin(\theta)=-\frac{5}{12}$

substitute

$(-\frac{5}{12})^2+cos^2(\theta)=1$

$\frac{25}{144}+cos^2(\theta)=1$

$cos^2(\theta)=1-\frac{25}{144}$

$cos^2(\theta)=\frac{119}{144}$

$cos(\theta)=\frac{\sqrt{119}}{12}$ ---> is positive (IV Quadrant)

step 3

Find the value of $tan(\theta)$

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

substitute the values

$tan(\theta)=-\frac{5}{12} : \frac{\sqrt{119}}{12}=-\frac{5}{\sqrt{119}}$

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3 years ago

The area of a circle is 1441 m2. What is the diameter of the circle?

gregori [183]

Hey there! I'm happy to help!

The area of a circle is the radius squared multiplied by pi (we will use 3.14). We already have the area, so we will go backwards.

1441÷3.14≈458.9171975

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√458.9≈21.42235275

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21.42235275×2=42.8447055

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use a graphing calculator or other technology to answer the question which quadratic regression equation best fits the data set

Greeley [361]

Answer:

Option C is the correct option.

In other words, the quadratic regression $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ is also attached.

Step-by-step explanation:

x y

3 470

4 416

5 403

Analyzing Option A:

Considering the equation

$y=32.86\:\left(x\right)^2+379.14\left(x\right)-1369.14\:$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2+379.14\left(3\right)-1369.14\:$

$y=64.02$

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2+379.14\left(4\right)-1369.14\:\:$

$y=673.18$

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2+379.14\left(5\right)-1369.14\:$

$y=1348.06$

Analyzing Option B:

$y=32.86\:\left(x\right)^2-379.14\left(x\right)$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2-379.14\left(3\right)$

$y=-841.68$

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2-379.14\left(4\right)$

$\:y=-990.8$

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2-379.14\left(5\right)$

$\:y=-1074.2$

Analyzing Option C:

Considering the equation

$y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2-379.14\left(3\right)+1369.14\:$

$y=527.46$

So, the approximately result is (3, 527)

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2-379.14\left(4\right)+1369.14\:$

$y=378.34$

So, the approximately result is (4, 378)

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2-379.14\left(5\right)+1369.14\:\:\:$

$y=294.94$

So, the approximately result is (5, 295)

Analyzing Option D:

Considering the equation

$y=-1369.14\:\left(x\right)^2-379.14\left(x\right)+32.86$

From (3, 470), putting x = 3

$y=-1369.14\:\left(3\right)^2-379.14\left(3\right)+32.86\:\:$

$y=-13426.82$

From (4, 470), putting x = 4

$y=-1369.14\:\left(4\right)^2-379.14\left(4\right)+32.86$

$y=-23389.94$

From (5, 403), putting x = 5

$y=-1369.14\:\left(5\right)^2-379.14\left(5\right)+32.86\:\:$

$y=-36091.34$

Therefore, from the above calculations and analysis, we conclude that Option C is the correct option.

In other words, the quadratic regression $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ is also attached.

3 0

3 years ago