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 :
idont know whis one is right
method # 1:
suppose b= 8, c=10,a=?
a^2+b^2=c^2
a^2=(10)^2-(8)^2=
100-64=36
taking sqaur root of 36
a=6
method #2
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
then B+C-180=A
.45+35-180=144.5
A=144.5
using law of sin
sin 35/10=sin 144.5/a
=10.12
a=10.12
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.
how does B= 27.3 how did u come up with that number
thanks
To find the distance of the tanker from the farther dock, we can use the concept of trigonometry and the given information.
Method #1:
Let's assume that the distance of the tanker from the farther dock is represented by "a". Using the Pythagorean theorem, we can set up the equation:
a^2 + 8^2 = 10^2
Simplifying this equation:
a^2 + 64 = 100
a^2 = 36
a = √36
a = 6
Therefore, the distance of the tanker from the farther dock is 6 km.
Method #2:
Let's assign variables to the angles and sides:
A = unknown (the angle opposite side "a")
B = unknown
C = 35 degrees
a = unknown
b = 8 km
c = 10 km
Using the law of sines:
sin A / a = sin C / c
Plugging in the values:
sin A / a = sin 35 / 10
Let's solve for A:
sin A = (a * sin 35) / 10
A = sin⁻¹((a * sin 35) / 10)
We know that the angles in a triangle sum up to 180 degrees. Therefore:
A + B + C = 180
Solving for B:
B = 180 - A - C
Now, we substitute the value of B into the law of sines equation to find A:
sin B = (b * sin A) / a
sin (180 - A - C) = (8 * sin A) / a
Simplifying the equation:
sin (144.5 - A) = (8 * sin A) / a
Now, we can solve for A by estimating the value of A that satisfies this equation. Once A is found, we can calculate the distance a using the law of sines:
sin A / a = sin C / c
By estimating these values, the distance of the tanker from the farther dock can be determined.