The exterior angle theorem states that the sum of two opposite interior angles is equal to the measure of the exterior angle.
The distance SL= 5.77 miles between the boat and the lighthouse after travelling 2.1 miles
According to the conditions given in the problem the exterior angle is 70 degrees and one of the opposite interior angle is 35 degrees.
m∠ L + m∠R= 70°
m∠ L + 35° = 70°
m∠ L = 70°-35°
m∠ L = 35°
If one interior angle is 35 degrees the other must also be 35 degrees to make a total of 70 degrees.
The sum of all angles of the triangle is always equal to 180 degrees.
So the third angle of the triangle will be
180°= 35°+35°+m ∠S
m∠S= 110°
From the triangle
Angle theta= m∠S= 110°
Fy= SL= height
Fx= RS = base
F= RL= hypotenuse
The line SL has to be found out.
Let the Fx= 2.1 miles
Then
Fx= Fcos ∅
But Cos ∅ = Cos 110°= -0.342
2.1= F (-0.342)
F= - 6.140 = hypotenuse
Now the vertical component
Fy= Fsine theta
Fy= - 6.140 sine 110°
Fy= - 6.14×0.94
Fy= -5.77 miles
The negative sign indicates that it is in the opposite direction.
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