sin problem?

Question

law of sines word problem:

an aircraft was attempting to fly from city A to city B but the course had a 10 degree error. after flying a distance of 50 miles, the pilot corected the course by turning at point C and flying 70 miles further. there was a constant speed of 250 miles per hour. How much time was lost?

I have no clue how to solve this! please help.

alpha= 10 degrees

I hope this helps.

Answer 1

Aww... must you use the law of sines? The law of cosines is much better, so I'll show you both methods:

But first, let me modify your note at the bottom to read:
alpha (α) = 10 degrees
(If I have read the problem correctly.)

First, the law of sines:
Recall sin(α) / A = sin(β) / B
Well, we know α is opposite side CB, and we'll say that β is opposite side AC (and likewise γ opposite AB):
sin(α) / A = sin(β) / B
β = arcsin (( Since α, β, and γ form the three angles of a triangle, we can thus assume:
α + β + γ = 180°
And now solve for γ, which using the law of sines again, we can solve for
Now, using the law of cosines:
c² = a² + b² + 2*a*b*cos(γ) where γ is the angle opposite side c.
Since α=10° is the only angle we know, we'll let c be the side opposite that (
Once you have the distance between points A and B, then you can compare that to the distance traveled along the path AC + CB, and compare their respective times (assuming the plane flies at a constant speed).

Good luck! Hope this helps!