Answer:
The distance between the two airplanes (to the nearest mile) is 1058 miles.
Step-by-step explanation:
An airplane A is at a location 800 miles due west of city X. So AX = 800 miles.
Another airplane is at a distance of 1,200 miles southwest of city X. So BX = 1200 miles.
The angle at city X created by the paths of the two planes moving away from city X measures 60°. So angle ∠AXB = 60°.
In triangle ΔAXB, AX = 800 miles, BX = 1200 miles, ∠AXB = 60°.
Using law of cosines:-
AB² = AX² + BX² - 2 * AX * BX * cos(∠AXB).
AB² = 800² + 1200² - 2 * 800 * 1200 * cos(60°).
AB² = 640000 + 1440000 - 2 * 960000 * 1/2
AB² = 2080000 - 960000
AB² = 1120000
AB = √(1120000) = 1058.300524
Hence, the distance between the two airplanes (to the nearest mile) is 1058 miles.
The measure of angle A is 144.3 degrees and the angle to cut the molding is 54.3 degrees
<h3>How to solve for angle A?</h3>
Start by solving the acute part of angle A using the following sine function
sin(Ax) = (30 - 4)/32
Evaluate the quotient
sin(Ax) = 0.8125
Take the arc sin of both sides
Ax = 54.3
The measure of angle A is then calculated as:
A = 90 + Ax
This gives
A = 90 + 54.3
Evaluate
A = 144.3
Hence, the measure of angle A is 144.3 degrees
<h3>The angle to cut the molding</h3>
In (a), we have:
Ax = 54.3
This represents the angle where the molding would be cut
Hence, the angle to cut the molding is 54.3 degrees
Read more about angles at:
brainly.com/question/1592456
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D≈2π(6371-1737.5)
d≈9267π
d≈29113.1km (to nearest tenth of a kilometer)
Answer:
(600 miles) / (3 hours) = 200 miles/hour
= 321.8 km/h
The answer would be 13 1/2 because you turn the 12 into a fraction then change the division sign into a multiplication sign and find the reciprocal of 8/9 which is 9/8 you could now divide 12/1 divided by 9/8 you could cross simply then dove to get 27/2 and in the end you get 13 1/2 if you turn the improper fraction into a mixed number.
