Download Tangent Ratio

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MPM 2D1
Trigonometry
Name: _____________
Date: ________________
PREPARATING FOR RIGHT TRIANGLE TRIGONOMETRY
LABELING ANGLES AND SIDES IN TRIANGLES
Recall that the angle measurements in a triangle add up to _________________.
Labeling Angles and Sides in Triangles:
In a triangle, each vertex is labeled with a ___________________ letter.
Each side is labeled with the _____________________________ letter
__________________ the vertex. Alternately, a side can be named using the
letters that identify its endpoints.
A
C
B
Angles may be labeled using the symbol _____ plus a single letter if it is obvious
which angle we are talking about. Otherwise, we use the ____ symbol plus three
letters to indicate the angle.
A
B
C
Example 1:
Label the sides in ∆MNO, then fill in the blanks below with the appropriate angle
names.
___________ or ____________ = 35º
___________ or ____________ = 90 º
___________ or ____________ = ____
Sides in a Right Triangle
Recall that a ________ triangle must have one ___________ angle (that is, an
angle that is equal to __________).
The side ____________________ the right angle is called the
_____________________. It is also the __________________ side in a right
triangle.
If we are considering <A, we would label side ____ as the side ______________
to <A, and side _______ as the side __________________ to <A.
A
C
B
If we are considering <C, we would label side ____ as the side ______________
to <C, and side _______ as the side __________________ to <C. Side ____
would still be labeled as the ____________________.
A
C
B
Example 2:
For each triangle, label the hypotenuse, opposite, and adjacent sides for the
marked angle.
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MPM 2D1
Trigonometry
Name: _____________
Date: ________________
THE TANGENT RATIO IN A RIGHT TRIANGLE
For each similar triangle, calculate the following ratio: the side opposite <A over
the side adjacent to <A.
BC

AC
DE

AE
H
F
D
8
B
FG

AG
HI

AI
6
4
2
A
3
C 3
E
3
G
3
All ratios are ______________________. The ratios depend only on the measure of
________________, not on the sizes of the triangle. We call this ratio the
_________________________ ratio of <A, and write it as _____________.
The Tangent Ratio of an Angle:
If <A is an acute angle (___________________) in a __________ triangle, then
tan A = _______________= ________________
A
C
B
I
Example 1:
Determine tan 32º, rounded to 4 decimal places. Draw a diagram to explain the meaning of the
result.
Example 2:
Calculate the length of BC to the nearest tenth of a centimetre.
A
3
240
B
C
A
Example 3:
3.2
In triangle PQR,
a) Calculate tan A and <A.
B
7.3
C
b) Calculate tan C and <C.
Example 4:
A guy wire supports a tower. The wire forms and angle of 54 with level ground. The wire is
attached to the ground 14.5 m from the base of the tower.
a) At what height is the guy wire attached to the tower?
b) How long is the guy wire?
Do pg. 362 Q 1-10