Use your knowledge of trigonometric ratiosto solve the following real-world situations.

1. An overhead crane is suspended from a ceiling by two chains. One chain is4.6 m long and forms an angle of60 with the ceiling. The other chain is6.4 m long.What angle does the larger chain make with the ceiling?

2.At noon, two tracking stations on Earth, 20 km apart, measure the angles of elevation of a rocket that was launched with a weather satellite. From Station A, the angle of elevation is41 and from Station B it is75 Find the altitude of the rocket to the nearest tenth. Note: Both tracking stations are on the same side of the rocket.

3. A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is435 mto the second vertex and 656 m to the third vertex. The angle between the lines of sight to the second and third vertices is 49 Calculate how much fencing he would need to enclose his entire field.

4.A balloonist at an altitude of 226 m observes the angles of depression of one point on the ground as 2 and of another point as3.The horizontal angle between the lines of sight to the two points is80 . What is the distance between the two points?