Tammy leaves the office, drives 26km due north, then turns onto a second highway and continues in a directiion of 30.0 degrees north of east for 62km. What's her total displacement from the office?

I can't quite understand how to do this since there's no 90 degree angle. The textbook went over it but I didn't get it at all... any help would be apprietiated. Thank you!

The resultant vector is the distance from the office. There doesn't have to be a 90 degree angle.

1. You know the distance from the office to the turn.
2. Start at the turn and create a triangle using a continuation of the northbound road, the 30 degree angle. At the end of the 62 km, drop a perpendicular to the northbound extension. That will give you your right triangle. You then want to construct the final vector from the origin to the endpoint. You will have two right triangles to solve.

Huh??

Tammy leaves the office, drives 26km due north, then turns onto a second highway and continues in a directiion of 30.0 degrees north of east for 62km. What's her total displacement from the office?

I can't quite understand how to do this since there's no 90 degree angle. The textbook went over it but I didn't get it at all...any help would be apprietiated. thank you!

In this situation you know a pattern of information

Side angle side!

Use the law of cosines to figure out the missing side

c^2=a^2+b^2-2abcos(\theta_c)

where c is the unknown length, a and b are the sides given, and \theta_c is the angle opposite side c.