26=2y-14 plz help out thxs :)

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

2 years ago

A(n-3)+8=bn solve for n

Lelu [443]

I am pretty sure this is right

6 0

2 years ago

Read 2 more answers

Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number

katrin [286]

The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.

<h3>What is a 2-digit number?</h3>

A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.

A 2-digit number is any number between 10 and 99.

According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.

1001 - 994 = 7 (1 digit)
1002 - 994 = 8 (1 digit)
1004 - 994 = 10 (2 digit)

Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.

Learn more about number at: brainly.com/question/17429689

#SPJ1

8 0

1 year ago

These solids all have the same volume. Which has the least surface area?

ipn [44]

Answer: I’m not sure, but I think it is solid C.

Step-by-step explanation: Please, make sure you have some knowledge when you answer this question. My answer is an educated guess. I do not want to be responsible for your wrong answers.

4 0

2 years ago

An online music club sells songs for $.95each plus a $1.95monthly fee for the service. If Maria’s total monthly bill was $14.30,

aksik [14]

First you would subtract the monthly fee from the total bill
$14.30 - 1.95 = 12.35$
Maria spend $12.35 on songs, to find out how many songs, you divide that by $.95
$12.35 \div .95 = 13$
Maria bought 13 songs this month.

5 0

2 years ago