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3 years ago

the sum of the angle measures triangle is 180⁰ find the measures of each angle in the triangle below

Mathematics

1 answer:

Dvinal [7]3 years ago

5 0

Answer:

∠ABC= 82°

∠ACB= 82°

∠BAC= 16°

Step-by-step explanation:

∠ABC +∠ACB +∠BAC = 180° (∠ sum of △ABC)

(5x -3)° +(5x -3)° +(x -1)°= 180°

5x -3 +5x -3 +x -1= 180

11x -7= 180 (simplify)

11x= 180 +7 (+7 on both sides)

11x= 187

x= 187 ÷11

x= 17

∠ABC

= (5x -3)°

= [5(17) -3]°

= 82°

∠ACB

= ∠ABC

= 82°

∠BAC

= (17 -1)°

= 16°

Alternatively,

∠BAC

= 180° -82° -82°

= 16°

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Se tiene un lote baldío de forma triangular bardeado. La barda de enfrente tiene una medida de 4 m,las otras dos bardas no es po

dybincka [34]

Answer:

a) La medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m. b) El triángulo en cuestión no es un triángulo rectángulo, es decir, ninguno de sus ángulos internos es recto (90 grados sexagesimales). En estos casos, no se puede aplicar el Teorema de Pitágoras o la simple utilización de las razones trigonométricas; se aplican, en cambio, leyes para la resolución de triángulos oblicuángulos (o triángulos no rectángulos).

Step-by-step explanation:

Este problema no se puede resolver "aplicando sólo las razones trigonométricas o el teorema de Pitágoras" porque es sólo aplicable a triángulos rectos, es decir, uno de los ángulos del triángulo es recto o igual a 90 grados sexagesimales. Los dos restantes triángulos suman 90 grados sexagesimales, o se dice, son complementarios.

La resolución de triángulos que no son rectos (conocida en algunos textos como solución de problemas de triángulos oblicuángulos) pueden resolverse usando, la ley de los senos (o teorema del seno), ley de los cosenos y la ley de las tangentes. El caso propuesto en la pregunta se ajusta a la ley de los senos:

$\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)}$

Es decir, la razón entre el lado de un triángulo y el seno del ángulo que tiene frente a él es igual para todos los lados y ángulos del triángulo.

El triángulo de la pregunta no tiene un ángulo recto

La suma de los ángulos internos de un triángulo es de 180 grados sexagesimales:

$\\ \alpha + \beta + \gamma = 180^{\circ}$

En la pregunta tenemos que la suma de los dos ángulos propuestos es:

$\\ 34^{\circ} + 64^{\circ} + \gamma = 180^{\circ}$

$\\ 98^{\circ} + \gamma = 180^{\circ}$

Restando 98 grados sexagesimales a cada lado de la igualdad:

$\\ 98^{\circ} - 98^{\circ} + \gamma = 180^{\circ} - 98^{\circ}$

$\\ 0 + \gamma = 180^{\circ} - 98^{\circ}$

$\\ \gamma = 82^{\circ}$

Con lo que se deduce que no hay ningún ángulo recto en el triángulo propuesto y no se podría usar el Teorema de Pitágoras o simples razones trigonométricas para resolverlo.

Resolución del lado del triángulo

De la pregunta tenemos:

La barda de enfrente tiene una medida de 4m. El ángulo que está enfrente de esta barda (barda frontal) es de 34°.
No se sabe el valor del lado que está enfrente del ángulo de 64°, pero se puede calcular usando la Ley de los senos.

Digamos que:

$\\ a = 4m, \alpha = 34^{\circ}$

$\\ b = x, \beta = 64^{\circ}$

Entonces, aplicando la Ley de los senos:

$\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)}$

Multiplicando a cada lado de la igualdad por $\\ \sin(\beta)$

$\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = \frac{b}{\sin(\beta)}*\sin(\beta)$

$\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*\frac{\sin(\beta)}{\sin(\beta)}$

$\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*1$

$\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b$

Sustituyendo cada valor en la expresión anterior:

$\\ b = \frac{a}{\sin(\alpha)}*\sin(\beta)$

$\\ b = \frac{4m}{\sin(34^{\circ})}*\sin(64^{\circ})$

$\\ b = 4m*\frac{0.8988}{0.5592}$

$\\ b = 6.4292m$

En palabras, la medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m.

El lado c puede obtenerse de manera similar considerando que $\\ \gamma = 82^{\circ}$ .

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3 years ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

The 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Step-by-step explanation:

The confidence interval of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the level of significance $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the z-score corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative standard normal table, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a normal distribution. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

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tester [92]

Answer:

its all sides are equal and diagonal make 90° angle.

so, the answer option c.

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3 years ago

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Law Incorporation [45]

Mary has 48 stickers. The ratio is 4:7

divide 48 with 4

48/4 = 12

Multiply 12 with 7

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Answer:

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3 years ago

the sum of the angle measures triangle is 180⁰ find the measures of each angle in the triangle below ​

the sum of the angle measures triangle is 180⁰ find the measures of each angle in the triangle below