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3 years ago

Solve the triangle. A = 46°, a = 34, b = 27

Mathematics

2 answers:

PtichkaEL [24]3 years ago

8 0

Answer:

All sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°

Step-by-step explanation:

In a given triangle A = 46°, a = 34 units and b = 27 units

Then we have to find all angles and measure of the side left.

By sine rule,

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{a}{sinA}=\frac{b}{sinB}$

$\frac{34}{sin46}=\frac{27}{sinB}$

sinB = $\frac{27\times sin46}{34}$

sinB = 0.5712

B = $sin^{-1}(0.5712)$

B = 34.83°

Since in a triangle,

∠A + ∠B + ∠C = 180°

46°+ 34.83° + ∠C = 180°

80.83° + ∠C = 180°

∠C = 180 - 80.83 = 99.17°

$\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{27}{sin34.83}=\frac{c}{sin99.17}$

$\frac{27}{0.5711}=\frac{c}{0.9872}$

c = $\frac{27\times 0.9872}{0.5711}=46.67$

Therefore, all sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°

WITCHER [35]3 years ago

4 0

Find the length of the hypotenuse

34^2 + 27^2 = c^2

1156 + 729 = 1885

c^2 = 1885

sqrt(1885)

c = 43.42

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Step-by-step explanation:

Data given

Our notation on this case :

$n_1 =60$ represent the sample size for people who used a self service

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$\sigma^2_1 =\sigma^2_2 =\sigma^2$

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$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

System of hypothesis

Null hypothesis: $\mu_1 \geq \mu_2$

Alternative hypothesis: $\mu_1 < \mu_2$

This system is equivalent to:

Null hypothesis: $\mu_1 - \mu_2 \geq 0$

Alternative hypothesis: $\mu_1 -\mu_2 < 0$

We can find the pooled variance:

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The degrees of freedom are given by:

$df=60+72-2=130$

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