How Far East Must a Biker Travel to Reach His Destination?

[dance_sg]

Homework Statement

A biker travels from a town due north along a secondary road. If the cabin he is going to is 100km N 20o W of the town, how far east will he have to travel when he reaches the east/west road?

Homework Equations

Sine,Cos,Tan, a^2+b^2=c^2

The Attempt at a Solution

i tried drawing this question out, but i can't seem to understand what it is I am suppossed to do..

 

[dance_sg]

nevermind. i figured it out.

 

[tomcue]

I would approach this problem by using basic trigonometry principles and the given information to find the distance the biker will have to travel east when he reaches the east/west road. First, I would draw a diagram to visualize the situation and label the given information. Then, I would use the given angle of N 20o W to determine the angle between the north direction and the direction the biker will have to travel to reach the cabin.

Next, I would use the trigonometric function tangent (tan) to find the distance the biker will have to travel east. By using the given angle and the distance of 100km, I can set up the equation tan(20o) = x/100km, where x represents the distance the biker will have to travel east. Solving for x, I get x = 100km * tan(20o). This gives me a distance of approximately 36.4km that the biker will have to travel east to reach the cabin.

In conclusion, by using basic trigonometry principles and the given information, I have determined that the biker will have to travel approximately 36.4km east to reach the cabin. It is important to note that this solution assumes a straight path from the town to the cabin, and the actual distance may vary depending on the specific route the biker takes.