Transcript MTH 112 Elementary Functions - Blue Mountain Community College

MTH 112
Elementary Functions
Chapter 5
The Trigonometric Functions
Section 2 – Applications of Right Triangles
Standard Labeling of Triangles
B
The right angle is angle C.
The acute angles are A and B.
The sides use the same lower
case letter as their opposite
angle.
A
c
b
a
C
Reminder: Definitions of
Trigonometric Functions of Acute
Angles of Right Triangles
O = opposite
A = adjacent
H = hypotenuse
Oscar Had
A Heap
Of Apples.
H
O

sin  = O/H
cos  = A/H
tan  = O/A
A
SOHCAHTOA  Sin = Opp / Hyp; Cos = Adj / Hyp; Tan = Opp / Adj
“Solving” Right Triangles
 Using given information about the
lengths of sides and/or measures of
angles of a triangle, find the lengths of all
of the sides and the measures of all the
angles of the triangle.
“Solving” Right Triangles
 Case 1: Given the lengths of two sides.

Use the Pythagorean Theorem to find the length of the
third side.

Use a trig function to find the measure of one of the
acute angles ().

Calculate the measure of the other acute angle (90°-).
NOTE: If possible, only use the given information in ALL calculations.
“Solving” Right Triangles
 Case 2: Given the length of one side and the
measure of one acute angle ().

Calculate the measure of the other acute angle (90°-).

Use a trig function to find the length of one of the other
sides.

Use a trig function to find the length of the third side.
NOTE: If possible, only use the given information in ALL calculations.
“Solving” Right Triangles
 Case 3: Given the measure of both acute angles.

Not enough information! Why?
Application Problems: Strategy
1. Get to know the problem.
a.
b.
c.
d.
e.
Read the problem.
Draw and label a picture or diagram.
Write down what you know.
Identify the unknowns (give them names).
Identify the question.
Application Problems: Strategy
1. Get to know the problem.
2. Find an equation or inequality that
relates the known and unknown
quantities.
Application Problems: Strategy
1. Get to know the problem.
2. Find an equation or inequality that
relates the known and unknown
quantities.
3. Solve the equation and state your
answer in terms of the problem (i.e.
answer the question).
Application Problems: Strategy
1. Get to know the problem.
2. Find an equation or inequality that
relates the known and unknown
quantities.
3. Solve the equation and state your
answer in terms of the problem (i.e.
answer the question).
4. Check your answer (i.e. does it make
sense in terms of the problem).
Types of Applications Using the
Trig Functions and Right Triangles
 Distances between objects or places.
 Angles of elevation & depression to
determine the altitude or height of an
object.
 Navigation.

Bearing
Version 1: Degrees east or west from north or
south (examples: N25°E or S40°W)
 Version 2: Degrees clockwise from north.

NOTE: Remember, all of these problems will involve a right triangle.