splash screen. lesson menu five-minute check (over lesson 8–6) ngsss then/now new vocabulary...
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Five-Minute Check (over Lesson 8–6)
NGSSS
Then/Now
New Vocabulary
Example 1:Write Vectors in Component Form
Example 2:Find the Magnitude and Direction of a Vector
Key Concept: Equal, Opposite, and Parallel Vectors
Key Concept: Vector Addition
Example 3:Vector Addition and Subtraction
Example 4:Real-World Example: Algebraic Vectors
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Over Lesson 8–6
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 50.1
B. 44.6
C. 39.3
D. 35.9
Find s if the measures of ΔRST are mR = 63, mS = 38, and r = 52.
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Over Lesson 8–6
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 21.3
B. 24.1
C. 29
D. 58
Find mR if the measures of ΔRST are mS = 122, s = 10.8, and r = 5.2.
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Over Lesson 8–6
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 12.7
B. 10.8
C. 9.62
D. 8.77
Use the measures of ΔABC to find c to the nearest tenth.
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Over Lesson 8–6
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 21°
B. 19°
C. 18°
D. 16°
Use the measures of ΔABC to find mB to the nearest degree.
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Over Lesson 8–6
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 21 mi
B. 18 mi
C. 16 mi
D. 15.5 mi
On her delivery route, Gina drives 15 miles west, then makes a 68° turn and drives southeast 14 miles. When she stops, approximately how far from her starting point is she?
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LA.1112.1.6.1 The student will use new vocabulary that is introduced and taught directly.
MA.912.D.9.3 Use vectors to model and solve application problems.
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You used trigonometry to find side lengths and angle measures of right triangles. (Lesson 8–4)
• Find magnitudes and directions of vectors.
• Add and subtract vectors.
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• vector
• standard position
• component form
• magnitude
• direction
• resultant
• parallelogram method
• triangle method
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Write Vectors in Component Form
Write the component form of .
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Write Vectors in Component Form
Find the change of x-values and the corresponding change in y-values.
Component form of vector
Simplify.
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Write the component form of .
A.
B.
C.
D.
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Find the Magnitude and Direction of a Vector
Find the magnitude and direction of for S(–3, –2) and T(4, –7).
Step 1 Use the Distance Formula to find thevector’s magnitude.
Distance Formula
Simplify.
Use a calculator.
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Find the Magnitude and Direction of a Vector
Graph to determine how to find the direction. Draw a right triangle that has as its hypotenuse and an acute angle at S.
Step 2 Use trigonometry to find the vector’sdirection.
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Find the Magnitude and Direction of a Vector
Simplify.
Substitution
Use a calculator.
tan S
Definition of inverse tangent
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Find the Magnitude and Direction of a Vector
A vector in standard position that is equal to forms a –35.5° degree angle with the positive x-axis in the fourth quadrant. So it forms a angle with the positive x-axis.
Answer: has a magnitude of about 8.6 units and a direction of about 324.5°.
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 4; 45°
B. 5.7; 45°
C. 5.7; 225°
D. 8; 135°
Find the magnitude and direction of for A(2, 5) and B(–2, 1).
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Vector Addition and Subtraction
Subtracting a vector is equivalent to adding its opposite.
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Vector Addition and Subtraction
Method 1 Use the parallelogram method.
Step 2 Complete the parallelogram.
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Vector Addition and Subtraction
Step 3 Draw the diagonal of the parallelogram from the initial point.
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Vector Addition and Subtraction
Method 2 Use the triangle method.
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Vector Addition and Subtraction
Answer:
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. B.
C. D.
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Algebraic Vectors
CANOEING Suppose a person is canoeing due east across a river at 4 miles per hour. If the river is flowing south at 3 miles an hour, what is the resultant direction and velocity of the canoe?
The initial path of the canoe is due east, so a vector representing the path lies on the positive x-axis 4 units long. The river is flowing south, so a vector representing the river will be parallel to the negative y-axis 3 units long. The resultant path can be represented by a vector from the initial point of the vector representing the canoe to the terminal point of the vector representing the river.
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Algebraic Vectors
Use the Pythagorean Theorem.Pythagorean Theorem
Simplify. Take the square root of each side.
The resultant velocity of the canoe is 5 miles per hour.Use the tangent ratio to find the direction of the canoe.
Use a calculator.
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Algebraic Vectors
The resultant direction of the canoe is about 36.9° south of due east.
Answer: Therefore, the resultant vector is 5 miles per hour at 36.9° south of due east.
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A. A
B. B
C. C
D. D
A B C D
0% 0%0%0%
A. Direction is about 60.3° south of due east with a velocity of about 8.1 miles per hour.
B. Direction is about 60.3° south of due east with a velocity of about 11 miles per hour.
C. Direction is about 29.7° south of due east with a velocity of about 8.1 miles per hour.
D. Direction is about 29.7° south of due east with a velocity of about 11 miles per hour.
KAYAKING Suppose a person is kayaking due east across a lake at 7 miles per hour. If the lake is flowing south at 4 miles an hour, what is the resultant direction and velocity of the canoe?
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