Download Tangent Ratio

MPM2D1 7.3:
Opening Activity:
The Trigonometric Ratios/ Tangent, Sine and Cosine
Read the instructions and answer the following questions:
1. Four nested right triangles are drawn
on the grid.
A
B
a) What angle is common to all four
triangles?
C
b) State the following lengths:
DF = 3 units
EF =
CG =
D
EG =
E
BH =
EH =
AI =
EI =
F
G
H
I
c) Determine the lengths of DE, CE, BE, and AE using the Pythagorean Theorem.
d) Complete the following chart. Put the ratios in lowest terms.
Triangle
EDF
ECG
EBH
EAI
Ratio Type 1
DF

EF
CG

EG
BH

EH
AI

EI
Ratio Type 2
DF

DE
CG

CE
BH

BE
AI

AE
Ratio Type 3
EF

DE
EG

CE
EH

BE
EI

AE
e) How are the Type 1 Ratios related?
f) This ratio is called the tangent ratio for angle E. How would you clearly and
accurately explain to someone which sides of the triangles you used to form the
tangent ratio? Use a sketch as well if necessary.
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Note: The trigonometric ratios depend only on the size of the angle, not on the size of
the triangle!
Example 1.
Find the Tangent Ratio from Given Sides
Find tan ø for each triangle, expressed as a fraction and as a decimal correct to four
decimal places.
6.8
b. θ
13
5
a.
4.5
8.2
12
Example 2
Find the Tangent of an Angle
Evaluate each of the following with a calculator. Record your answer rounded to four
decimal places.
a) tan 300
b) tan 500
c) tan 750
Example 3
Find an Angle Using the Tangent Ratio
Flora is building a skateboarding ramp. She wants the ramp to rise 1 m in a
horizontal distance of 2 m . At what acute angles should she cut the wood, rounded to the
nearest degree?
2
Example 4
Find a Side length using the Tangent Ratio
Find the length x, in the diagram, rounded to the nearest of a centimeter.
9.5
x
250
Example 5
Solve a Multi-Step Problem Using the Tangent Ratio
A radio transmitter is to be supported with a guy wire. The wire is to form a 650
angle with the ground and reach 30 m up the transmitter.
The wire can be ordered in whole- number lengths of metres. How much wire should
be ordered? Draw the diagram first.
p. 361CYU #3
Practice #1ace, 34ace, 6-7ac, 9, 10,
11,13,14,15,17
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