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3 years ago

Use the law of Sines to find the missing angle of the triangle. Find m

Mathematics

1 answer:

Whitepunk [10]3 years ago

6 0

Ah...Trigonometry is fun!

The law of sines states:
$\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}$
The transitive property (switching the orders of the equations) applies here. Therfore, we can say that $\frac{sinA}{a}=\frac{sinC}{c}$

We then plug in our given values to find C

$\frac{sin24}{77}=\frac{sinC}{162}$
$\frac{162*sin24}{77}=sinC$
Solving, we get 0.8557316387. We're not done yet!

We are trying to find an angle measure, so we'll do the inverse of the ratio we used (sin).

arcsin0.8557316387 (arcsin is the same as inverse sin)
=58.8 (approximate)

So the measure of angle C is 58.8. You could check this by reinserting it into the equation $\frac{sinA}{a}= \frac{sinB}{b} = \frac{sinC}{c}$ .

:)

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If the mass of a material is 44 grams and the volume of the material is 6 cm^3, what would the density of the material be?

Svetlanka [38]

Density is mass per unit volume.

For the given material that has a mass of 44 grams occupying a volume of 6 cm^3, we divide the mass by the volume, i.e.

density of material = 44 grams / 6 cm^3 = 44/6 grams/cm^3 = 7.3 g/cm^3 (to two significant figures)

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3 years ago

I need help.6\10 - 1\2?

spin [16.1K]

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6/10 - 5/10 = 1/10 <==

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3 years ago

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What is the leading coefficient of the function f(x)= 3x^5+6x^4-x-3

Natali5045456 [20]

3. The leading coefficient of the function f(x)= 3x⁵+6x⁴-x-3 is 3.

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3 years ago

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is

frozen [14]

Answer:

The decision rule for rejecting the null hypothesis is $t < -1.721$

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:

$H_0: \mu = 410$

At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:

$H_0: \mu < 410$

Type of test:

As we test if the mean is less than a value, we have a left-tailed test.

We have the standard deviation for the sample, which means that the t-distribution is used.

We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.

Using a calculator, the critical value is $t_c = -1.721$

Determine the decision rule for rejecting the null hypothesis.

We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is $t < -1.721$

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3 years ago

After robbing a bank in dodge city, a robber gallops off at 14 mi/h. 20 minutes later, the marshall leaves to pursue the robber

Morgarella [4.7K]

For this case we have to write the equation of the position of each one.

We have then:

For the robber:

$r = 14t$