2 2.1.3 Quiz: Naming Triangles by Angle Measures

A surveyor wants to find the distance from points A and B to an inaccessible point C. These three points form a triangle. Becaus

harkovskaia [24]

Answer:

Part a) $AC=135.95\ m$

Part b) $BC=124.14\ m$

The diagram in the attached figure

Step-by-step explanation:

step 1

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

$m\angle A+m\angle B+m\angle C=180^o$

substitute the given values

$53^o+61^o+m\angle C=180^o$

$114^o+m\angle C=180^o$

$m\angle C=180^o-114^o$

$m\angle C=66^o$

step 2

Find the distance AC

Applying the law of sines

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

see the attached figure to better understand the problem

substitute the given values

$\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}$

$AC=\frac{142}{sin(66^o)}(sin(61^o))$

$AC=135.95\ m$ ---> rounded to the nearest hundredth

step 3

Find the distance BC

Applying the law of sines

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

substitute the given values

$\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}$

$BC=\frac{142}{sin(66^o)}(sin(53^o))$

$BC=124.14\ m$ ---> rounded to the nearest hundredth

4 0

3 years ago

Minor surgery on horses under field conditions requires a reliable short-term anesthetic producing good muscle relaxation, minim

andreev551 [17]

Answer:

$p_v =P(t_{74}$

If we compare the p value and a significance level for example $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.

Step-by-step explanation:

Data given and notation

$\bar X=18.81$ represent the average lateral recumbency for the sample

$s=8.4$ represent the sample standard deviation

$n=75$ sample size

$\mu_o =20$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to apply a left tailed test.

What are H0 and Ha for this study?

Null hypothesis: $\mu \geq 20$

Alternative hypothesis : $\mu < 20$

Compute the test statistic

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{18.81-20}{\frac{8.4}{\sqrt{75}}}=-1.227$

The degrees of freedom are given by:

$df=n-1=75-1=74$

Give the appropriate conclusion for the test

Since is a one side left tailed test the p value would be:

$p_v =P(t_{74}$

Conclusion

If we compare the p value and a significance level for example $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean it's not significantly less than 20 min.

3 0

3 years ago

Which sentence can represent the inequality box+ 204?

Black_prince [1.1K]

Answer:

first one

Step-by-step explanation:

is at least

5 0

3 years ago

Describe in detail how you would create a number line with the following points: 1, 3.25, the opposite of 2, and – (–4fraction o

kipiarov [429]

Answer:

points 4 , 1 ,25 , opposite of 3 , -1/2To Find

Step-by-step explanation:

3 0

2 years ago

Dan buys pure silver to make jewelry. The graph shows the relationship between the amount of money Dan spent on pure silver and

Luda [366]

The answer is quite straightforward...

That's $56 per 80 grams.

($56)/(80g)

Explanation:

$\left( { x }_{ 1 },{ y }_{ 1 } \right) =\left( 0,0 \right) \\ \\ \left( { x }_{ 2 },{ y }_{ 2 } \right) =\left( 80,\quad 56 \right) \\ \\ \therefore \quad \frac { Rise }{ Run } =\frac { 56-0 }{ 80-0 } =\frac { 56 }{ 80 }$

4 0

3 years ago

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