Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Two baseball players are warming up by throwing balls to the catcher. The two players are located $10$ yards apart, and the angle from each player to the catcher is $55^{\circ}$ and $71^{\circ}$ , respectively. What is the distance from the farthest baseball player to the catcher? $\newline$ A. $10.125$ yards $\newline$ B. $11.687$ yards $\newline$ C. $14.501$ yards $\newline$ D. $14.790$ yards

View step-by-step help

View step-by-step help

Interpret measures of center and variability

Full solution

Q. Two baseball players are warming up by throwing balls to the catcher. The two players are located

10

yards apart, and the angle from each player to the catcher is

55^{\circ}

and

71^{\circ}

, respectively. What is the distance from the farthest baseball player to the catcher?

\newline

A.

10.125

yards

\newline

B.

11.687

yards

\newline

C.

14.501

yards

\newline

D.

14.790

yards

Understand and Visualize: Understand the problem and visualize the scenario. $\newline$ We have a triangle where the distance between the two baseball players is one side, and the distances from each player to the catcher form the other two sides. The angles given are from each player to the catcher. We need to find the distance from the farthest player to the catcher, which is opposite the largest angle.
Use Law of Sines: Use the law of sines to set up the equation. $\newline$ The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Let's denote the distance from the farthest player to the catcher as $d$ , the distance between the players as $a = 10$ yards, and the angles as $\alpha = 55^\circ$ and $\beta = 71^\circ$ . The angle opposite the side we want to find is $\gamma = 180^\circ - \alpha - \beta$ .
Calculate Opposite Angle: Calculate the angle opposite the side we want to find. $\newline$ $\gamma = 180^\circ - 55^\circ - 71^\circ$ $\newline$ $\gamma = 180^\circ - 126^\circ$ $\newline$ $\gamma = 54^\circ$
Apply Law of Sines: Apply the law of sines to find the distance $d$ . $\newline$ Using the law of sines: $\newline$ $\frac{a}{\sin(\gamma)} = \frac{d}{\sin(\beta)}$ $\newline$ $\frac{10}{\sin(54^\circ)} = \frac{d}{\sin(71^\circ)}$
Solve for Distance: Solve for $d$ . $\newline$ $d = \frac{10 \cdot \sin(71^\circ)}{\sin(54^\circ)}$ $\newline$ Now we calculate the sine values and solve for $d$ . $\newline$ $d \approx \frac{10 \cdot 0.9455}{0.8090}$ $\newline$ $d \approx \frac{9.455}{0.8090}$ $\newline$ $d \approx 11.687$ yards

More problems from Interpret measures of center and variability

Question

Michael surveyed

2

politicians from his state about their views on certain issues.

\newline

Is this sample of citizens of the state likely to be biased?

\newline

\newline

\newline

Posted 1 month ago

Question

Read the following description of an experiment.

\newline

A massage therapist has received complaints that the fragrance of her massage oil is unpleasant. She is testing whether a new oil will improve each clients' experience.

\newline

The massage therapist randomly sorts her clients into two groups. She massages

5

clients from the first group with the new oil and

5

from the other group with her usual oil. She asks all

10

clients to rate their massages.

\newline

Is this experiment statistically well designed?

\newline

\newline

\newline

Posted 1 month ago

Question

A random sample of

35

four-door passenger vehicles had a mean gas mileage, in miles per gallon

(\mathrm{mpg})

25.9 \mathrm{mpg}

. The estimate had a margin of error of

2.6 \mathrm{mpg}

98 \%

confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles?

\newline

1

\newline

24 \mathrm{mpg}

\newline

29 \mathrm{mpg}

\newline

32 \mathrm{mpg}

\newline

35 \mathrm{mpg}

Posted 2 months ago

Question

1

578

randomly selected American adults,

44.8 \%

of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of

2.5 \%

95 \%

confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls?

\newline

1

\newline

40 \%

\newline

43 \%

\newline

48 \%

\newline

95 \%

Posted 4 months ago

Question

Malik walked up and back down an empty

18 \mathrm{~m}

long escalator at a constant rate. Since the escalator was going up at the time, it took him only

22.5 \mathrm{~s}

. Going down took Malik

90

s. Assume the escalator speed is constant.

\newline

What was Malik's walking speed?

\newline

\frac{\mathrm{m}}{\mathrm{s}}

Posted 2 months ago

Question

Select the outlier in the data set.

\newline

74,84,86,87,89,91,92,98,126

Posted 2 months ago

Question

p

\begin{array}{l}\frac{p}{8}=\frac{7}{9} \\p=\square\end{array}

Posted 2 months ago

Question

Jelani needs to hire at least

12

artists for an upcoming event. He needs to hire visual artists, who will be paid

\$300

for the event, and performers, who will be paid

\$480

for the event. His budget for paying the artists is no more than

\$6,000

. He must hire at least

4

visual artists and at least

3

performers. Which of the following does not satisfy all of the conditions described?

\newline

1

\newline

4

visual artists and

10

\newline

8

visual artists and

8

\newline

\$300

0

visual artists and

3

\newline

\$300

2

visual artists and

4

Posted 2 months ago

Question

\newline

k^2 + 9k + 18

\newline

\newline

Posted 2 months ago

Question

18

\newline

The population of Greenville increased by

7 \%

2015

2016

2016

k

2015

population, what is the value of

k

Posted 17 hours ago