Solving Right Triangles: Problems 2

Problem : Two boats leave the same port. One goes 10 miles due west and drops anchor. The other leaves the port 20 degrees north of west. How far must it go in a straight line to get as far west as the first boat?

x = 10 sec(20)

10.64. The second boat must travel about 10.6 miles to get as far west as the first boat.

Problem : A man flies a kite with a 100 foot string. The angle of elevation of the string is 52^o. How high off the ground is the kite?

x = 100 sin(52)

78.8. The kite is about 79 feet above the ground.

Problem : An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplane flies over the building.

x = arctan(

)

5.72^o. The plane must take off at an angle of elevation of about 5.72^o in order to avoid hitting the building.

Problem : A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?

x = arcsin(

)

68.3^o. The ladder must be situated with about a 68.2^o angle of elevation in order to reach the top of the wall.

Problem : A ramp is needed to allow vehicles to climb a 2 foot wall. The angle of elevation in order for the vehicles to safely go up must be 30^o or less, and the longest ramp available is 5 feet long. Can this ramp be used safely?