Homework #2

Homework due in class, Oct 15. Show your work, neatly.

1) Using the sine formula, determine missing angles in sides of the following spherical triangles. (6 points)

2) Using the cosine and sine formula, find the missing angles and sides for the following table (hint: use the cosine formula to find the missing side, then the sine formla to find the missing angles): (8 points)

3) In the Islam faith, one of a Muslim's duties is to perform the salat (prayer) five times a day. This is recited while orienting one's body towards Mecca. Assuming that one wants to orient along a great circle toward Mecca, what angle from true North must an individual in Eugene face for salat? (4 points)

4) Find the distance between Helsinki and Seattle along the shortest route. Where is the northernmost point of the route, and what is its distance from the North Pole? Helsinki is at 25° E and 60° N, Seattle is 122° W and 48° N. The radius of the Earth is 6370 km. Draw a detailed diagram. (6 points)

5) Two places, A and B, on the same parallel of latitude 38° 33^' N are 123° 19^' apart in longitude. Calculate in kilometers (i) their distance apart along the parallel, (ii) the great circle distance AB. Draw a diagram. (6 points)

6) Calculate the distance between stars A and B on the horizon system. (6 points)