All categories

3 years ago

Use the Law of Sines to find the measure of angle J to the nearest degree.

Mathematics

1 answer:

rjkz [21]3 years ago

8 0

$\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
-----------------------------\\\\
\cfrac{sin(J)}{9.1}=\cfrac{sin(97^o)}{11}\implies sin(J)=\cfrac{9.1\cdot sin(97^o)}{11}
\\\\\\
\textit{now taking }sin^{-1}\textit{ to both sides}
\\\\\\
sin^{-1}\left[ sin(J) \right]=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right)
\\\\\\
\measuredangle J=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right)$

You might be interested in

A country is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30

kondaur [170]

Answer:

We conclude that speed is greater than 30 miles per hour.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 30 miles per hour

Sample mean, $\bar{x}$ = 35 miles per hour

Sample size, n = 15

Alpha, α = 0.01

Sample standard deviation, s = 4.7 miles per hour

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30\text{ miles per hour}\\H_A: \mu > 30\text{ miles per hour}$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{35 - 30}{\frac{4.7}{\sqrt{15}} } = 4.120$

Now, $t_{critical} \text{ at 0.01 level of significance, 14 degree of freedom } = 2.624$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis and conclude that speed is greater than 30 miles per hour.

We calculate the p-value.

P-value = 0.00052

Since p value is lower than the significance level, we reject the null hypothesis and accept the alternate hypothesis. We conclude that speed is greater than 30 miles per hour.

6 0

3 years ago

Determine the measure of the interior angle at vertex C

vladimir1956 [14]

The measure of the interior angle at vertex C is D. 144.

<h3>How to calculate the angle?</h3>

Based on the information given, the angle will be calculated thus:

8x + 8x + 8x + 3x + 3x = (5 - 2) × 180

30x = 540

Divide both side by 30

30x/30 = 540/30

x = 18

Therefore, at vertex C, we have 8x. This will be:

= 8x

= 8 × 18

= 144

Learn more about angles on:

brainly.com/question/13007711

#SPJ1

5 0

2 years ago

Which quadrant of the coordinate plane has ordered pairs in the form of a positive number

Setler [38]

Answer:

Quadrant IV

Step-by-step explanation:

On the graph, the x-axis numbers are positive and the y-axis numbers are negative

8 0

3 years ago

Can you please help me with this I been stuck for a long time

yarga [219]

Answer:

Step-by-step explanation:

2.671 = (2.67 × 100)(1 × 100) = 267100. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 267100 is also equal to 267100 when expressed as a mixed number.

3 0

3 years ago

15. Robin ordered pizza and opted for delivery.

Ivenika [448]

Answer: No she'll need atlease 9 dollars

Step-by-step explanation:

48.95 x 18% is 8.811 which is greater than

4 0

2 years ago