Download Problems using Similar Triangles

Lesson Plan
Grade 10 Academic Math
Lesson:
Unit: Trigonometry
7 - 2___
Topic: Problems using Similar Triangles
homework check: Principles of Mathematics 10 p. 378 # 4 – 6, 8, 11 – 13
note: Problems using Similar Triangles
Similar triangles can be used to determine measurements that cannot be measured
directly using standard techniques. This process is called indirect measurement. We continue to
use the proportions of similar triangles to solve for unknown side lengths. It is important to note
that the scale factor of one corresponding side to another can be used to multiply any other side
to find the measure. For example, in the diagram
D
51
A
6.0 cm
51
1.2 cm
1.1 cm
59
59
B
1.0 cm
E
C
F
The triangles are similar because two angles are equal, therefore, the ratio of side AB to
DE should be the same for each of the other sides. Essentially, we want to know the scale factor
‘n’.
DE
n=
AB
6
=
1.2
=5
Therefore, if we multiply each of the sides by 5, we find the missing measures.
Side EF = 1(5) = 5 cm and side DF = 1.1(5) = 5.5 cm.
Solving word problems involving diagrams that must be drawn requires some definition.
An angle of inclination (or elevation) is an angle that rises from the horizontal. An angle of
depression is an angle that falls from the horizontal.
A new bridge is going to be built across a river, but the width of the river is unknown and
cannot be measured directly. Surveyors set up posts are points A, B, C, D, and E and took the
measurements relative to the posts. Find the width of the river.
B
river
C
A
9m
D
50 m
13 m
E
Step 1: establish similarity
< A = < D and < C = < C in each triangle, therefore the triangles are similar.
Step 2: establish order of similarity
triangle ABC = triangle DEC
Step 3: solve for unknown measure
AC AB
=
DC DE
50 AB
=
9
13
13 ( 50 )
= AB
9
AB = 72m
Therefore, the river is 72 m wide.
homework assignment: Principles of Mathematics 10 p. 386 # 2, 4, 5, 7, 9, 11 – 13