Download 5-1 Right Triangle Trigonometry 2016

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
8.2 cm
4.5 cm
4.2 cm
3.1 cm
1.7 cm
7.6 cm
10.9 cm
6.6 cm
10.1 cm
7.1 cm
2.7 cm
4.1 cm
Verify that the four triangles above are similar and write the similarity statements.
Round to the nearest 1000th.
Length of
the leg
opposite
the 22°
angle
Length of the
leg adjacent
to the 22°
angle
Length of the
hypotenuse
ΔABC
ΔDEF
ΔHIJ
ΔLMN
Calculate the
mean of each
column.
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.
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:
sine       side
angle 
cosine    side
angle 
tangent    side
side
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.
5.8 cm
29◦
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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 ) ?
Practice
1. Find the below ratios:
2.
Solve for x
3.
Solve for mA
1a. sin  X  
1b. tan  X  
1c. cos  Z  
HOMEWORK:
7. mH  ______ 8. mL  ______
7.
cos1 0.48 __________
8. sin 1 0.42 __________
9. tan 1 0.5 __________
C. Solve for the variables. Round to the nearest 100th.
OVER 
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7.