ENGR 52
Lab 2: Trig and Systems of Eqns
Trigonometry Problems -- solve 1
1) Steve is training for a career in building and is learning how to use a ladder safely. He
has to consider two distances: • the distance of the foot of the ladder from the wall • the
height of the top of the ladder up the wall. The ratio of these two distances must be 1:4
a) Show that the angle between the ladder and the wall is 14° to the nearest degree.
b) Steve’s ladder is 5 metres long. How far from the wall should he place the foot of the
ladder? Give your answer to an appropriate level of accuracy.
c) Show how you used a different method to check your answer to part b.
2) While working in Greenland, a lost scientist radios back to base for help. Command station 1
receives the radio signal at an angle of 50 degrees West of North. Station 2 receives the signal at
an angle of 20 degrees East of North. Both stations are on an E-W line, and Station 1 is 10 miles
E of Station 2.
a) How far away is the scientist from Station 1? From Station 2?
b) The rescue team calls in their position, located midway between station1 and 2. What heading
should they be instructed to travel in to reach the lost scientist?
3) For the following Piston problem, we’ll solve some simpler questions
a) Suppose L1 = .5 feet and L2 = 1.4 feet. What is the maximum distance from the crankshaft
the end of L2 can reach?
What is the minimum distance?
b) Find the distance of the end of L2 from the crankshaft for angle A = 45 degrees, 90 degrees
and 135 degrees.
Systems of Equations – Solve 1
4)
An airplane flying into a headwind travels the 1800-mile flying distance between two cities
in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the
air speed of the plane and the speed of the wind, assuming that both remain constant.
5)
Ten gallons of a 30% acid mixture is obtained by mixing a 20% solution with a 50%
solution. How much of each must be used?
6)
Five hundred tickets were sold for a certain music concert. The tickets for the adults and
children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were
$3,312.50. How many of each kind of ticket were sold?
7)
The standard equation of a circle is
circle that passes through the points
Find the equation of the
,
, and
8)
Five hundred tickets were sold for a certain music concert. The tickets for the adults sold for
$7.50, the tickets for the children sold for $4.00, and tickets for senior citizen sold for $3.50. The
revenue for the Monday performance was $3,025. Twice as many adult tickets were sold as
children tickets. How many of each ticket was sold?
9) TRIG CHALLENGE !! First person to solve wins the treat for the day!
Move the robot arm to relocate all 5 pucks from the start to the end positions shown:
START
FINISH
As shown below, to arrive at position -9,0 the motors positions should be
theta1= 2.0376, theta2= 2.2081
And to arrive at position 12,12 as shown below, the motor angles should be set to 0.2278 1.1152