Two airplanes leave an airport at the same time, the first headed due north and the second at a bearing of N42^ E . At 2:00PM, the first airplane is 312 miles from the airport while the second airplane is 487 miles from the airport. Assuming both followed linear paths from the airport, how far apart are the two airplanes at 2:00PM?

Answer:

The two airplanes are about 330miles apart.

Step-by-step explanation:

The diagram interpreting the question has been attached to this response.

As shown in the diagram,

i. the airplanes leave at point C.

ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.

iii. the points A, B and C form a triangle with sides a, b and c.

To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.

c² = a² + b² - 2abcosC            --------------(i)

where;

b  = 312miles

a = 487miles

C = 42°

Substitute these values into equation (i) and solve as follows;

c² = (487)² + (312)² - 2(312)(487)cos(42)

c² = (237169) + (97344) - 303888cos(42)

c² = (237169) + (97344) - 303888(0.7431)

c² = 334513 - 225819.1728

c² = 108693.8272

Take the square root of both sides

√c² = √108693.8272

c = 329.69

c ≅ 330miles

Therefore, the two airplanes are far apart by 330miles

what is the volume of the rectangular prism?​ will give brainliest

Customary American Units of Weight
1 pound = 16 ounces
1 ton = 2,000 pounds or 32,000 ounces

Convert:
130 ounces = pounds ounces

Need help on this please

In a lab experiment, 8700 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 25 hours. How long would it be, to
the nearest tenth of an hour, until there are 19100 bacteria present?

A roulette wheel has 383838 slots, of which 181818 are red, 181818 are black, and 222 are green. In each round of the game, a ball is tossed in the spinning wheel and lands in a random slot. Suppose we watch 777 rounds of this game, and let RRR represent the number of rounds where the ball lands in a red slot.

Element X is a radioactive isotope such that every 6 years, its mass decreases by a half. Given that the initial mass of a sample of
Element X is 46 grams, write a function to model the mass of the element.

What is the slope of the two points (-20,-4), (-12,-19)

I need he answer pls {WIIL MARK BRAINLIST}

The court has two stone hoops. each is 15 feet high on the wall. A player is 6 feet away from a hoop. what's the diagonal distance from his feet to the hoop.​

A group of adults were surveyed about whether they prefer to carpool or take the bus to work. Which conclusions can be drawn from the results of the survey? Check all that apply. A person in the group who is a man is more likely to carpool. Carpool Bus A person in the group who is a woman is more likely to carpool. Men 51% 49% A person in the group who is a man is more likely to take the bus. There is no association between commuting preferences and gender. Women 49% 51% Total 100% 100%​

Three less than two times a number is 55. What is the number?
​

4/5 of the magnets in George's collection are flags. 1/2 of those flags are U.S. flags.

What fraction of George's magnets are U.S. flags?

You are a school photographer taking individual and class pictures for 2 classes of 21 students each. On average, each individual picture takes 3 minutes and a class picture takes 10 minutes. About how long should it take you to take all of the pictures? A 1 hour 3 minutes B 1 hour 13 minutes C 2 hours 6 minutes D 2 hours 16 minutes E 2 hours 26 minutes

elementary math! please help Mark brainlist​

The hypotenuse of a right triangle will be a diameter of the triangle. True or false?

for a March past competition on sports day the house captain of one house cut 25 pieces of ribbon each 1/2 metre in length.what was the length of ribbon cut altogether​

Trent grew 12 plants with 4 seed packets. With 5 seed packets.
how many plants can he grow?

Find the volume of cylinder

9 gal and 1 pt - 2pt

The County Fair features rides, exhibitions, and games of chance. Luca decides to play Wheel of Letters. To play the game, contestants spin a wheel with 26 equal sections, lettered A through Z. If the pointer lands on any letter in the phrase “COUNTY FAIR,” the contestant wins a prize.
Part B:
Of the first 52 contestants, exactly 12 contestants win the game. How does the actual number of winners compare to the expected number of winners? What needs to happen for the experimental probability to approach the theoretical probability? Explain.

Pls pls pls pls help pls

Cooper invested $3,100 in an account paying an interest rate of 2%
compounded quarterly. Robert invested $3,100 in an account paying an
interest rate of 3 % compounded continuously.After 12 years, how much
more money would Robert have in his account than Cooper, to the nearest
dollar?

A beach volleyball court is 9 meters wide and 17 meters long. The rope used for the boundary line costs $4.00 per meter. How much would it cost to buy a new boundary line for the court?

can you find the volume for this pls.

i need help on this TT

Find the length of side x in simplest radical form with a rational denominator.

five different names were put into a hat. A name is chosen 111 times and the name Karen is chosen 29 times. What is the experimental probability of the name Karen being​ chosen? What is the theoretical probability of the name being​ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.

I know this does have to do with school or math but does anyone know if baking soda can clarify your hair

In a cookie jar there are 9 sugar cookies and 12 snickerdoodle cookies. The cookie are randomly mixed together in the jar. What is the probability of pulling two of the same types of cookies out of the cookie jar in a row without replacement?

Manesh is putting new tile on a kitchen counter. Each sheet of tile will cover 1.5 ft squared. How many sheets of tile will Manesh need to cover the whole counter?