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Pachacha [2.7K]
3 years ago
14

Find the measures of the angles of the triangle ABC if measure of angle A:measure of angle B:measure of angle C = 2:3:4.

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
8 0

Answer:

Angle A = 40

Angle B = 60

Angle C = 80

Step-by-step explanation:

The three angles of a triangle are in the ratio

2:3:4

Multiply by x

2x:3x:4x

The sum of the angles is 180 degrees

2x+3x+4x = 180

9x = 180

Divide by 9

9x/9 = 180/9

x = 20

The value of x is 20

A         B       C    

2*20:3*20:4*20

40       60    80

Angle A = 40

Angle B = 60

Angle C = 80

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Answer:

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Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

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Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a pvalue of 1 - 0.05 = 0.95, so Z = 1.645.

Now, find the margin of error M as such

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In which \sigma is the standard deviation of the population and n is the size of the sample.

How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?

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4 = 1.96\frac{\sigma}{\sqrt{n}}

4\sqrt{n} = 1.96\sqrt{\sigma}

\sqrt{n} = \frac{1.96\sqrt{\sigma}}{4}

(\sqrt{n})^2 = (\frac{1.96\sqrt{\sigma}}{4})^2

n = (\frac{1.96\sqrt{\sigma}}{4})^2

The minimum sample size needed is n = (\frac{1.96\sqrt{\sigma}}{4})^2. If n is a decimal number, it is rounded up to the next integer. \sigma is the standard deviation of the population.

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Sedaia [141]

Answer:

Part 1) BC=12.2\ units

Part 2) m\angle A=55^o

Part 3) m\angle C=35^o

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

AC^2=AB^2+BC^2

substitute the given values

AC^2=7^2+10^2

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Part 2) Find the measure of angle A

we know that

In the right triangle ABC

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substitute the values

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using a calculator

m\angle A=tan^{-1}(\frac{10}{7})=55^o

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

m\angle A+m\angle C=90^o ----> by complementary angles

substitute the given value

55^o+m\angle C=90^o

m\angle C=90^o-55^o=35^o

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