PARCC Assessment Readiness UNIT 8 Review/Test Organizer Objective: Provide review and practice for chapters and standardized tests. Standard Items MCC9-12.G.SRT.6 3, 7, 8, 9, 10, 11, 12, 13, 17, 19, 23 MCC9-12.G.SRT.7 2, 18 MCC9-12.G.SRT.8 1, 4, 5, 6, 14, 15, 16, 20, 21, 22, 24 Resources Assessment Resources Unit Assessment Go to my.hrw.com for updated online PARCC-aligned Assessment Readiness. PARCC Assessment Readiness Selected Response 1. The length of one leg of a right triangle is 3 times the length of the other, and the length of the hypotenuse is 10. What is the length of the longest leg? 3 3 √10 √10 12 √5 2. Which of the following is NOT equivalent to sin 60°? cos 30° √ 3 _ 2 (cos 60°)(tan 60°) tan 30° _ sin 30° 3. △ABC is a right triangle. m∠A = 20°, m∠B = 90°, AC = 8, and AB = 3. Which expression can be used to find BC? 3 _ tan 70° 8 _ sin 20° 8 tan 20° 3 cos 70° 4. A slide at a park is 25 ft long, and the top of the slide is 10 ft above the ground. What is the approximate measure of the angle the slide makes with the ground? 21.8° 23.6° 66.4° 68.2° 5. Tell if the measures 6, 13, and 14 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse. Yes; acute triangle Yes; obtuse triangle Yes; right triangle No. 6. Find all the values of k so that (-3 , 4), (-8, 5), and (-5, k) are the vertices of a right triangle. k = -6, 1, 9, 20 k = -5, 2, 7, 19 k = -5, 1, 9, 19 k = -6, 2, 7, 20 7. △ABC is a right triangle in which m∠A = 30° and m∠B = 60°. Which of the following are possible lengths for the sides of this triangle? AB = √ 3, AC = √ 2, and BC = 1 AB = 4, AC = 2, and BC = 2 √ 3 AB = 6 √3, AC = 27, and BC = 3 √ 3 AB = 8, AC = 4 √3, and BC = 4 8. Find the values of x and y. Express your answers in simplest radical form. y 30º 60º 24 x x = 12, y = 12 √3 x = 12 √3, y = 12 x = 12, y = 12 √2 x = 12 √2, y = 12 UNIT 8 REVIEW/TEST 868 Unit 8 Review/Test 868 Unit 8 Review/Test
Transcript
PARCC Assessment ReadinessUNIT 8 Review/Test
OrganizerObjective: Provide review and practice for chapters and standardized tests.
Standard ItemsMCC9-12.G.SRT.6 3, 7, 8, 9, 10, 11, 12,
Go to my.hrw.comfor updated online PARCC-aligned Assessment Readiness.
PARCC Assessment Readiness
Selected Response 1. The length of one leg of a right triangle is 3
times the length of the other, and the length of the hypotenuse is 10. What is the length of the longest leg?
3
3 √10
√10
12 √5
2. Which of the following is NOT equivalent to sin 60°?
cos 30°
√ 3 _2
(cos 60°)(tan 60°)
tan 30°_sin 30°
3. △ABC is a right triangle. m∠A = 20°, m∠B = 90°, AC = 8, and AB = 3. Which expression can be used to find BC?
3_tan 70°
8_sin 20°
8 tan 20°
3 cos 70°
4. A slide at a park is 25 ft long, and the top of the slide is 10 ft above the ground. What is the approximate measure of the angle the slide makes with the ground?
21.8°
23.6°
66.4°
68.2°
5. Tell if the measures 6, 13, and 14 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse.
Yes; acute triangle
Yes; obtuse triangle
Yes; right triangle
No.
6. Find all the values of k so that (-3 , 4) , (-8, 5) , and (-5, k) are the vertices of a right triangle.
k = -6, 1, 9, 20
k = -5, 2, 7, 19
k = -5, 1, 9, 19
k = -6, 2, 7, 20
7. △ABC is a right triangle in which m∠A = 30° and m∠B = 60°. Which of the following are possible lengths for the sides of this triangle?
AB = √ 3 , AC =
√ 2 , and BC = 1
AB = 4, AC = 2, and BC = 2 √ 3
AB = 6 √ 3 , AC = 27, and BC = 3 √ 3
AB = 8, AC = 4 √ 3 , and BC = 4
8. Find the values of x and y. Express your answers in simplest radical form.
9. An architect designs the front view of a house with a gable roof that has a 45°-45°-90° triangle shape. The overhangs are 0.5 meter each from the exterior walls, and the width of the house is 16 meters. What should the side length l of the triangle be? Round your answer to the nearest meter.
0.5 m 0.5 m
16 m
l l
12 m
11 m
24 m
23 m
10. Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth.
15
12
9
X Z
Y
cos X = 12 _ 9
≈ 1.33
cos X = 9 _ 15
= 0.60
cos X = 12 _ 15
= 0.80
cos X = 9 _ 12
= 0.75
11. Use a special right triangle to write tan 60° as a fraction.
√ 3 _ 1
1 _ √ 3
√ 2 _ 1
√ 3 _ 2
12. Use your calculator to find the trigonometric ratios sin 79°, cos 47°, and tan 77°. Round to the nearest hundredth.
sin 79° = -0.99, cos 47° = -0.44, tan 77° = -32.27
sin 79° = -0.44, cos 47° = -0.99, tan 77° = -32.27
sin 79° = 0.68, cos 47° = 0.98, tan 77° = 4.33
sin 79° = 0.98, cos 47° = 0.68, tan 77° = 4.33
13. Find sin ∠A to the nearest hundredth.
A C
2
4
B
sin ∠A = 0.45
sin ∠A = 0.50
sin ∠A = 2.24
sin ∠A = 0.89
14. Some mountains in the Alps are very steep and have a grade of 42.7%. To the nearest degree, what angle do these mountains make with a horizontal line?
23°
67°
47°
32°
15. Classify each angle in the diagram as an angle of elevation or an angle of depression.
43
2
1
Angles of elevation: ∠1, ∠3Angles of depression: ∠2, ∠4
Angles of elevation: ∠2, ∠4Angles of depression: ∠1, ∠3
Angles of elevation: ∠1, ∠4Angles of depression: ∠2, ∠3
Angles of elevation: ∠2, ∠3Angles of depression: ∠1, ∠4
2 Points = The student’s answer is an accurate and complete execu-tion of the task or tasks.
1 Point = The student’s answer con-tains attributes of an appropriate response but is flawed.
0 Points = The student’s answer contains no attributes of an appropriate response.
Performance Task Rubric
Task Possible points
23. a 1 point for drawing a similar triangle and 1 point for indicating the lengths of the new triangle.
b 2 points for finding the values of the sine, cosine, and tangent of the given triangle.
Sample answer: For the given triangle,
sin 30° = 1 _ 2 , cos 30° =
√ 3 _
2 ,
tan 30° = 1 _ √ 3
, sin 60° = √ 3
_ 2 ,
cos 60° = 1 _ 2 , tan 60° = √ 3 .
c 2 points for finding the values of the sine, cosine, and tangent of the similar triangle.
For the similar triangle,
sin 30° = 5 _ 10
= 1 _ 2 ,
cos 30° = 5 √ 3
_ 10
= √ 3
_ 2 ,
tan 30° = 5 _ 5 √ 3
= 1 _ √ 3
,
sin 60° = 5 √ 3
_ 10
= √ 3
_ 2 ,
cos 60° = 5 _ 10
= 1 _ 2 , and
tan 60° = 5 √ 3
_ 5 = √ 3 .
Total possible points: 6
16. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.
20
25
The missing side length is 15. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation a 2 + b 2 = c 2 .
The missing side length is 32.02. The side lengths do not form a Pythagorean triple because one of them is not a nonzero whole number.
The missing side length is 5. The side lengths form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation a 2 + b 2 = c 2 .
The missing side length is 32.02. The side lengths form a Pythagorean triple because they satisfy the equation a 2 + b 2 = c 2 .
17. Find the value of x. Express your answer in simplest radical form.
5
x
x
x = 5 √ 2 _ 2
x = 5 √ 2
x = √ 5 √ 2 _
2
x = 5 √ 3 _ 2
18. Find the value of x that satisfies the equation sin (4x + 14) ° = cos (-3x + 73) °.
x = 3 _ 7
x = 3
x = 59 _ 7
x = 93
Mini-Tasks 19. Find the sine and cosine of the acute angles in the
right triangle.
B
A
53 45
28
20. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°. What is the horizontal distance between the eagle and its prey? Round to the nearest foot.
21. Mike is standing between Lani and the Eiffel Tower. He and Lani are 21.2 meters apart. From Mike’s position, the angle of elevation to the top of the Eiffel Tower is 40°. From Lani’s position, the angle of elevation to the top of the Eiffel Tower is 38.5°. How many meters high is the Eiffel Tower? Round to the nearest meter.
21.2 m
40°38.5°ML E
22. A building casts a shadow that is 85 ft long when the angle of elevation to the sun is 34°.
a. What is the height of the building? Round to the nearest inch and show your work.
b. What is the angle of elevation to the sun when the shadow is 42 ft 6 in. long? Round to the nearest tenth of a degree and show your work.
24. a 1 point for stating that the angle formed by North Boulevard and Main Street is a right angle and the triangle is a right triangle.
b 1 point for stating that the Pythagorean Theorem can be used to find the sides of a right triangle and 1 point for writing the equation:
10 2 + 15 2 = x 2
c 1 point for finding the length of the new street to the nearest mile and 1 point for converting the distance to the nearest foot.
10 2 + 15 2 = x 2
100 + 225 = x 2
x = √ 325 = 18.028 miles
There are 5280 feet in one mile, so the length of the new street is 18.028(5280) = 95,187 feet.
d 1 point for estimating the cost of constructing the new street.
The estimated cost is the length of the new street multiplied by the cost per linear foot, plus the cost of 2 intersections: 95,187(110) + 2(1,450,000). The estimated cost is $13,370,570. To the nearest thousand, the estimated cost is $13,371,000.
Total possible points: 6
Performance Tasks 23. A 30°-60°-90° triangle is shown below. Draw
another triangle similar to the given triangle, indicating the lengths of the sides. Show that the values of the sine, cosine, and tangent of the 30° and 60° angles of your triangle are the same as those for the given triangle.
2
3
30°
1
A C
B
24. A new street is going to be constructed to connect Main Street, which runs in the east-west direction, and North Boulevard, which runs in the north-south direction, as shown in the diagram below. The construction cost has been estimated at $110 per linear foot, excluding the new intersections. The intersections are estimated to cost $1,450,000 each.
10 mi
S
W E
15 m
i
Main Street
new
stre
et
No
rth
Blv
d.
Part A: What type of triangle is bounded by the new street, North Boulevard, and Main Street? How do you know?
Part B: Let x represent the length of the new street. What is the name of the formula that can be used to find the value of x? Use that formula to write an equation that can be solved for x.
Part C: What is the length of the new street to the nearest thousandth of a mile? Convert that distance to the nearest foot. Show your work.
Part D: Estimate the cost of constructing the new street. Be sure to include the costs for intersections. Show your work and round the cost to the nearest thousand dollars.
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