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2 years ago

Use the Law of Sines to find the missing angle of the triangle.

Mathematics

1 answer:

Natasha2012 [34]2 years ago

8 0

Answer:

m∠B = 70.0° (nearest tenth)

Step-by-step explanation:

<u>Sine Rule for Angles</u>

$\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

a = 13
c = 19
A = 40°

Substituting the given values into the formula to find m∠C:

$\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}$

$\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}$

$\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)$

$\implies \sf m \angle C=69.96086904^{\circ}$

Interior angles of a triangle sum to 180°

$\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}$

$\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}$

$\implies \sf m \angle B=70.03913...^{\circ}$

Therefore, m∠B = 70.0° (nearest tenth)

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What expression is equivalent to 2 m plus m plus m

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3 years ago

Is 2 times 176 equal to 4 times 38 true or fulse

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2 years ago

Read 2 more answers

The endpoints of a line segment are at the coordinates (–6, 3, 4) and (4, –1, 2). What is the midpoint of the segment?

natulia [17]

Answer:

$( - 1,1,3 )$

Step-by-step explanation:

Use the midpoint formula:

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )$

We want to find the midpoint of the line

that has endpoints.

$(\frac{ - 6+4}{2},\frac{3+ - 1}{2}, \frac{4+2}{2} )$

We simplify to get;

$(\frac{ - 2}{2},\frac{2}{2}, \frac{6}{2} )$

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The correct answer is A.

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2 years ago

A university administrator was interested in determining if there was a difference in the distance students travel to get from c

eduard

Answer:

1) Fail to reject the Null hypothesis

2) We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.

Step-by-step explanation:

A university administrator wants to test if there is a difference between the distance men and women travel to class from their current residence. So, the hypothesis would be:

$H_{o}: \mu_{F}-\mu_{M}=0\\\\ H_{a}: \mu_{F}-\mu_{M}\neq 0$

The results of his tests are:

t-value = -1.05

p-value = 0.305

Degrees of freedom = df = 21

Based on this data we need to draw a conclusion about test. The significance level is not given, but the normally used levels of significance are 0.001, 0.005, 0.01 and 0.05

The rule of the thumb is:

If p-value is equal to or less than the significance level, then we reject the null hypothesis
If p-value is greater than the significance level, we fail to reject the null hypothesis.

No matter which significance level is used from the above mentioned significance levels, p-value will always be larger than it. Therefore, we fail to reject the null hypothesis.

Conclusion:

We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.

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3 years ago

The growth of a strain of bacteria can be modeled by the function graphed, where the x-values are the time in seconds and the y-

Andrew [12]

There are (A) 2.7 bacterias initially.

<h3>What is a function?</h3>

A function is an expression that establishes the relationship between the dependent and independent variables.
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
The set X is known as the function's domain, while the set Y is known as the function's codomain.
Originally, functions were the idealization of how a variable quantity depends on another quantity.

To find the number of bacteria:

The graph shows that the function follows an exponential curve, and the starting point is at ( 0,2.7 ).
The starting number of bacteria is then 2.7.

Therefore, there are (A) 2.7 bacterias initially.

Know more about functions here:

brainly.com/question/25638609

#SPJ4

The correct question is given below:
The growth of a strain of bacteria can be modeled by

the function graphed, where the x-values are the time

in seconds and the y-values are the number of

bacteria. How many bacteria are there initially?

(A) 2.7

(B) 2.8

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1 year ago