January 06, 2012
Pre-Calculus
Notes 4.8 Applications and Models
Solving a right triangle: determine the measures of all the sides and all the angles in a triangle. Use trig
ratios to find the unknown sides and angles.
EX 1: Given B = 54012’ and
c = 15, solve the right
triangle.
EX 2: Find the altitude of an isosceles triangle with base angle 180 and base
= 10m.
January 06, 2012
Angle of Elevation – angle made with the horizontal looking up.
Angle of Depression – angle made with the horizontal looking down.
Application Problems:
EX 3: Height
A 100ft line is attached to a kite. When the kite has pulled the line taut, the angle of elevation to the kite is
approximately 500. Approximate the height of the kite.
EX 4: Angle of Elevation / Angle of Depression
At a point 150 ft from the base of a building, the angle of elevation to the bottom of a smokestack is 350, and the
angle of elevation to the top of the smokestack is 410. Find the height of the smokestack. (Assume the
smokestack is on the edge of the building.)
January 06, 2012
Day 2: More Applications
Example 1: An airplane leaves the runway, its angle of climb is 22
Find the plane’s altitude after 2 minutes.
0
and its speed is 325 ft/sec.
January 06, 2012
Example 2: Two Equations / Two Unknowns
A passenger in a plane is flying at an altitude of 10 km sees two towns directly to the east of the
plane. The angles of depression to the towns are 280 and 550. How far apart are the towns?
550 280
January 06, 2012
Example 3: Simple Harmonic Motion
Frequency - number of cycles per unit of time. F = 1 / Period.
An ocean buoy follows a simple harmonic motion pattern modeled by the equation:
Sketch the graph that the buoy follows and find the period, amplitude, maximum displacement,
and frequency of the function.
January 06, 2012
Navigation and Bearings
A bearing is the acute angle a path or line makes with the fixed NORTH-SOUTH
line.
a.) N 230 E
b.) S 570 W
E
S
N
N
N
W
c.) N 450 W
W
E
S
W
E
S
Nautical Miles = number of minutes in the angle measure (10 = 60’)
Knots = nautical miles per hour.
January 06, 2012
Example 4: A ship leaves port at noon and heads due west at 20 knots, or 20 nautical
miles per hour. At 2 pm, the ship changes course to N 50 W. Find the ship’s bearing and
distance from the port of departure at 3pm.
January 06, 2012