Download 5-1 intro to trig investigation

Math 2
Lesson 5-1: Right Triangle Trigonometry
Name ___________________________
Date __________________________
Learning Goals:
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I can use the Pythagorean Theorem to solve for an unknown side length of a right triangle.
I can use the characteristics of similar figures to justify the trigonometric ratios.
I can define the following trigonometric ratios for acute angles in a right triangle: sine, cosine,
and tangent.
I can calculate sine, cosine and tangent ratios for acute angles in a right triangle when given two
side lengths.
I can understand that if cos A = sin B, then A and B are complementary angles. I can explain
this using a picture of a right triangle.
I can use the angle measures to estimate side lengths.
I can use side lengths to estimate angle measures.
I. Prerequisite Skills for Trigonometry:
II. What is Trigonometry?
Trigonometry is
Vocabulary and symbols:
Opposite leg
Adjacent leg
Hypotenuse
Acute angles
α
Right angle
Pythagorean Theorem
Ratio
Complementary angles
β
θ
OVER 
Page 2
III. Ratios of Sides in Right Triangles
Verify that the four triangles above are similar and write the similarity statements.
Round to the nearest 100th.
Length of the
leg opposite
the 22° angle
to nearest 10th
of cm
ΔABC
ΔDEF
ΔHIJ
ΔLMN
Length of the leg
adjacent to the
22° angle to
nearest 10th of cm
Length of the
hypotenuse to
nearest 10th of cm
Length of
opposite leg
Length of
opposite leg
Length of
adjacent leg
÷
÷
÷
Length of
adjacent leg
Length of
hypotenuse
Length of
hypotenuse
Page 3
1. On the calculator, press c and choose #5 Settings and #2 Document Settings. Next scroll down to Angle
and choose Degree. Finally select Make Default at the bottom of the page.
2. Use your calculator to fill in the problems below: Round to 3 decimal places.
sin(22o )  ________
cos(22o )  ________
tan(22o )  ________
Look back at your computations in the table. Where do you see these same values?
3. Based on your measurements and computations from this worksheet complete the following definitions:
In any right triangle, where  is NOT the right angle:
angle 
sine    side
cosine    side
tangent    side
side
angle 
angle 
angle 
4. Mnemonic device to remember these ratios:
5. If you know a ratio of two side lengths, how can you find the acute angle measure?
In the figure below  A is a right angle. Round to 3 decimal places.
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Find the length of c using C.
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Find the length of c using B.
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What is the relationship between cos( B ) and sin(C ) ?
5.8 cm
29◦
OVER 
Page 4
HOMEWORK:
7. mH  ______ 8. mL  ______
7.
cos1 0.48 __________
8. sin 1 0.42 __________
C. Solve for the variables. Round to the nearest 100th.
4.
5.
8

7.52
6.
7.
9. tan 1 0.5 __________