PRE-CALCULUS /TRIGONOMETRY
Name _______________________
Objective:
a. Solve real-life problems involving right triangles;
b. Solve real-life problems involving directional bearings;
c. Solve real-life problems involving harmonic motion.
In solving problems related to triangles, you need to recall the following:
Pythagorean Theorem
SohCahToa
Law of Sines
Law of Cosines
You also need to know how to interpret ___________________ to solve navigation problems, and
analyze wave motion or ______________________ _____________________ when describing
objects that move with vibration, oscillation or rotation.
SohCahToa 1
A safety regulation states that the maximum angle of
elevation for a rescue ladder is 72°. A fire department’s
longest ladder is 110 feet. What is the maximum safe
rescue height?
SohCahToa 2
At a point 200 feet from the base of a building, the angle of
elevation to the bottom of a smokestack is 35°, whereas
the angle of elevation to the top is 53°. Find the height s
of the smokestack alone.
SohCahToa 3
A swimming pool is 20 meters long and 12 meters wide.
The bottom of the pool is slanted so that the water depth is
1.3 meters at the shallow end and 4 meters at the deep
end. Find the angle of depression of the bottom of the
pool.
Trigonometry and Bearings
A bearing measures the ______________ _______________ that a path or line of sight makes
with a fixed north-south line.
What is the bearing for each of the following diagrams?
Example: A ship leaves port at noon and heads due west at 20 knots. At 2 P.M. the ship changes
course to N 54° W. Find the ship’s bearing and distance from the port of departure at 3 P.M.
Harmonic Motion
Period = ________________________
Amplitude = _____________________
Frequency = ____________________
Example 1: Consider the ball on the end of the spring from the previous page. Suppose that
maximum distance the ball will travel upward or downward from its equilibrium position is 10 cm.
The time it takes for the ball to move from its maximum displacement above zero and back again
is t = 4 seconds.
(Assume ideal conditions of perfect elasticity and no friction or air resistance).
What is the frequency of this harmonic motion?
Example 2: Given the equation for simple harmonic motion as 𝑑 = 6𝑐𝑜𝑠
(a) the maximum displacement,
(b) the frequency,
(c) the value of d when t = 4, and
(d) the least positive value of t for which d = 0
3𝜋
4
𝑡 , find