The Captain of a freighter 8km fromthe nearer of two unloading docks on the shore finds that the angle between the lines of sight to the docks is 35 degrees. if the docks are 10km apart, how far is the tanker from the farther dock?
The Captain of a freighter 8km fromthe nearer of two unloading docks on the shore finds that the angle between the lines of sight to the docks is 35 degrees. if the docks are 10km apart, how far is the tanker from the farther dock?
My answers :
A= unknown
B= unknown
C=35 degrees
a=unkown
b=8km
c=10km
using law of sin
sin 35/10=sinB/8
=.45
B=.45 dgrees
drwls, Saturday, May 24, 2008 at 5:19pm
The law of sines is the way to do this. That is your method #2. Method #1 only applies to right triangles.
You made some algebra errors, however.
sin B = 0.4589
B = 27.3 degrees
180 - B - C = A , not what you wrote.
i didn't get how he got 27 for B can someone explain it please
Looks like you were cut-and-pasting one of drwls responses.
I also got
sin B = 0.4589
B = 27.3 degrees
You were wondering how he got that???
Are you sure you have your calculator set to 'degrees'?
Depending on your make of calculator, press
Shift or 2ndF sin, then .4589
your calc should give you 27.3º
To find the value of angle B, we can use the law of sines.
The law of sines states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant. In this case, we have the following information:
Angle C = 35 degrees (the angle between the lines of sight to the docks)
Side c = 10 km (the distance between the docks)
Side a = 8 km (the distance from the tanker to the nearer dock)
Side b = unknown (the distance from the tanker to the farther dock, which we want to find)
Now we can set up the equation using the law of sines:
sin C / c = sin B / b
Substitute the given values:
sin 35 / 10 = sin B / b
Now solve for sin B:
sin B = (sin 35 / 10) * b
To find the value of angle B, we need to take the inverse sine (arcsin) of both sides of the equation:
B = arcsin((sin 35 / 10) * b)
At this point, we don't know the value of b yet, so we cannot directly calculate B. However, we can rearrange the equation and solve for b:
b = (10 * sin B) / sin 35
Now we can substitute the given values and solve for b:
b = (10 * sin B) / sin 35
b = (10 * sin 27.3) / sin 35
Using a calculator, we find that sin 27.3 ≈ 0.4599 and sin 35 ≈ 0.5736.
Plugging in these values:
b ≈ (10 * 0.4599) / 0.5736
b ≈ 8 km
So, the distance of the tanker from the farther dock is approximately 8 km.