Problem 1: You stand at the bottom left corner of your property, which is shaped like a triangle. You look straight to your right and see the marker at the right corner of the bottom of your property. You then turn through an angle of 40o and look at the mailbox at the top corner of your property. You now walk 60 feet to the right corner at the bottom of your property. You look back at the left corner of the bottom of your property and then turn through an angle of 35o and look at the mailbox. How far is it from each each corner of your property to the mailbox?
Problem 2: You are designing a park that will be shaped like a triangle. It is bounded by three straight roads - Boros Boulevard, Luke Lane, and Gallagher Avenue. Boros Boulevard is 1.4 miles long, Luke Lane is 2.2 miles long, and the angle between them is 72o. How long is Gallagher Avenue?
Problem 3: If sina A = 5/13, and cos B = -(4/9), and both angles are in the second quadrant, find:
a) sin(A + B)
b) cos (A + B)
c) tan (A - B)
Problem 4: If cotθ = -(7/11), and tanφ = 9/7, with π/2 < θ < π and π < φ < 3π/2, find:
a) sin(θ - φ)
b) cos (θ + φ)
c) tan (θ + φ)