An equation is shown below:

A triangle has side lengths of 9 in, 13 in, and 20 in. What is the measurement of this triangle’s largest angle?

zvonat [6]

1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :

i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.

ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:

$a^{2}=b ^{2}+c ^{2}-2bc(cosA)$

2.

$20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA)

400=81+169-234(cosA) 150=-234(cosA)

cosA=150/-234= -0.641$

3. m(A) = Arccos(-0.641)≈130°,

4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc

4 0

3 years ago

Read 2 more answers

Which of the following probabilities is equal to approximately 0. 2957? Use the portion of the standard normal table below to he

Travka [436]

Probability of an event is the measure of its chance of occurrence. The event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

<h3>How to get the z scores?</h3>

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

$X \sim N(\mu, \sigma)$

(X is following normal distribution with mean $\mu$ and standard deviation $\sigma$ )

then it can be converted to standard normal distribution as

$Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)$

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

$P(Z \leq z) = P(Z < z) )$

Also, know that if we look for Z = z in z tables, the p-value we get is

$P(Z \leq z) = \rm p \: value$

Using the z-table, we get the needed probabilities as:

Case 1:

$P(-1.25 \leq Z \leq 0.25) = P(Z \leq 0.25) - P(Z \leq -1.25) \approx 0.5987 - 0.1056 = 0.4931$

Case 2:

$P(-1.25 \leq Z \leq 0.75) = P(Z \leq 0.75) - P(Z \leq -1.25) \approx 0.7734- 0.1056=0.6678$

Case 3:

$P(0.25 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.25) \approx 0.8944 - 0.5987=0.2957$

Case 4:

$P(0.75 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.75) \approx 0.8944 - 0.7734 =0.1210$

Thus, the event out of the listed events whose probability is 0.2957 is given by : Option C: $P(0.25 \leq Z \leq 1.25)$

Learn more about z-scores here:

brainly.com/question/13299273

5 0

2 years ago

5xy + 4yz + 3zx for x = -1, y =-3, z = 4

neonofarm [45]

Answer:

-45

Step-by-step explanation:

5 *-1 *-3= 15

4 *-3 *4= -48

3 *4 *-1=-12

15 -48 -12= -45

8 0

3 years ago

A cylinder has a volume of 360 in^3. If the height and radius are multiplied by 2.5, what will the resulting volume be?

4vir4ik [10]

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=2.5r\\
h=2.5h
\end{cases}\implies V=\pi (2.5r)^2(2.5h)
\\\\\\
V=\pi \cdot 2.5^2\cdot r^2\cdot 2.5h\implies V=(2.5^2\cdot 2.5)\pi r^2 h
\\\\\\
V=15.625\pi r^2h\impliedby \textit{15.625 of the original}
\\\\\\
\textit{if the original was 360}\qquad 15.265\cdot 360$

5 0

3 years ago

A conical paper cup has a radius of 2 inches. Approximate, to the nearest degree, the angle β (see the figure) so that the cone

Aneli [31]

I don't know where the angle β is, so I will make the assumption that tanβ = h/r
$V = \frac{1}{3} \pi r^{2} h$

V volume = 60
r radius = 2
h = r tanβ

$tan \beta = \frac{3V }{ \pi r^{3} } = \frac{ 180}{25,1} = 7,17 \\ \\ \beta = 82$

7 0

3 years ago