Explain thoroughly and show the complete solution. And please
sketch a picture every problem. It would really help me alot.
1.) The angle of elevation of a balloon from a station directly
south of it is 71.6 degrees. From a second station, 2.8 mi
directly E of the first one, the angle of elevation is 46.9 degrees.
If the instrument is 6 ft above the level ground, what is the
height of the balloon in feet?
2.) From the top of a tower, 380.5 ft above sea level, the angle
of depression of a boat which has a bearing of N 70.4 degrees E
was observed and found to be 32.6 degrees. Another boat,
bearing S 19.6 degrees E, had an angle of depression of 16.9
degrees. Find the distance between the boats.
3.) A ship is sailling on a straight course. A lighthouse is sighted
ahead, and it is noted that angle between a line to the lighthouse
and the ship’s course is 27 degrees. After travelling 2.65 km, the
ship has gone past to the lighthouse is now 420 degrees. How
close (to the nearest meter) did the ship come to the lighthouse?
4.) Airport B is 200 mi due East of airport A. To reach airport C,
a plane flies from A on a course of 346.35 degrees or from B on
a course of 302.2 degrees. Fine the distance from A to C and
from B to C.
5.) A ship leaves a small island on a course of 106 degrees. The
ship is travelling at 25 knot (nautical miles per hour). After 2
hours, the course is changed to 221 degrees. Some time later,
the ship receives a message to return to the island. To do so,
the ship turns to a heading of 33 degrees 30 minutes. What is
the total length of the trip ( in nautical miles)?
6.) A ship intends to sail from port A to port B at a distance of
359 mi. It sails at a constant speed of 35 mph. After 2 h, the
captain discovers that they have been sailling off course by 18
degrees. He then corrects the course. What is the total time of
7.) A plane leaves an airport and flies at 36 mph on a course of
103.25 degrees for 1 hour and 33 minutes. Then it changes
course to 236.75 degrees and flies for 48 minutes. How far is it
from the airport? If it wished to return, what would be its course?